Package 'gamlss.countKinf'

Generating and Fitting K-Inflated 'discrete gamlss.family' Distributions

Description

The main purpose of this package is to allow the user of the GAMLSS models to fit K-inflated discrete distributions.

Details

Package:	gamlss.countKinf
Type:	Package
Version:	3.5.1
Date:	2018-11-2

The user can generates K-inflated distrinutions from discrete gamlss.family for fitting gamlss model.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

Maintainer: Saeed Mohammadpour <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2003) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Examples

# generating one inflated distribution from SICHEL model
gen.Kinf(family=SICHEL, kinf=1)

# generating two inflated distribution from Delaporte model
gen.Kinf(family=DEL, kinf=1)

---

generates a K-inflated distribution from discrete gamlss family

Description

The gen.Kinf() function allows the user to generate d, p, q, and r K-inflated distribution functions plus an extra K-inflated from gamlss.family function for fitting a K-inflated distribution with gamlss.

Usage

gen.Kinf(family = "NO", kinf=1)

Arguments

family	a gamlss.family object, which is used to define the distribution for generating K-inflated model. The distribution families supported by gamlss() can be found in gamlss.family.
kinf	define inflated point in generating K-inflated distribution from discrete gamlss.family

Value

The functions gen.Kinf return d, p, q, and r K-inflated distribution functions and K-inflated distribution from discrete gamlss.family

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),

Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.

Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or see http://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Examples

# generate one inflated Negative Binomial distribution
gen.Kinf(family =NBI, kinf=1)

# generate one inflated Delaporte distribution
gen.Kinf(family =DEL, kinf=1)

# generate one inflated Sichel distribution
gen.Kinf(family =SICHEL, kinf=1)

---

K-inflated Beta Negative Binomial distributions for fitting a GAMLSS model

Description

The function KIBNB defines the K-inflated Beta Negative Binomial distribution, a four parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().The functions dKIBNB, pKIBNB, qKIBNB and rKIBNB define the density, distribution function, quantile function and random generation for the K-inflated Beta Negative Binomia, KIBNB(), distribution.

Usage

KIBNB(mu.link = "log", sigma.link = "log", nu.link = "log",
            tau.link = "logit", kinf="K")

dKIBNB(x, mu = 1, sigma = 1, nu = 1, tau = 0.1, kinf=0, log = FALSE)

pKIBNB(q, mu = 1, sigma = 1, nu = 1, tau = 0.1, kinf=0, lower.tail = TRUE,
            log.p = FALSE)

qKIBNB(p, mu = 1, sigma = 1, nu = 1, tau = 0.1, kinf=0, lower.tail = TRUE,
            log.p = FALSE, max.value = 10000)

rKIBNB(n, mu = 1, sigma = 1, nu = 1, tau = 0.1, kinf=0, max.value = 10000)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "log" link as the default for the nu parameter
tau.link	Defines the tau.link, with "logit" link as the default for the tau parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of nu
tau	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
max.value	a constant, set to the default value of 10000 for how far the algorithm should look for q

Details

The definition for the K-inflated Beta Negative Binomial distribution.

Value

The functions KIBNB return a gamlss.family object which can be used to fit K-inflated Beta Negative Binomial distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIBNB

Examples

#-------------------------------------------------------------------------------

KIBNB() # gives information about the default links for the  Beta Negative Binomial distribution
#-------------------------------------------------------------------------------

# generate zero inflated Beta Negative Binomial distribution
gen.Kinf(family=BNB, kinf=0)

# generate random sample from zero inflated Beta Negative Binomial distribution
x<-rinf0BNB(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the zero inflated Beta Negative Binomial distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0BNB, data=data)
histDist(x, family=inf0BNB)
## End(Not run)
#-------------------------------------------------------------------------------

# generated one inflated Beta Negative Binomial distribution
gen.Kinf(family=BNB, kinf=1)

# generate random sample from one inflated Beta Negative Binomial distribution
x<-rinf1BNB(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the one inflated Beta Negative Binomial distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1BNB, data=data)
histDist(x, family=inf1BNB)
## End(Not run)
#-------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2; tau=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1BNB(x, mu=mu, sigma=sigma, nu=nu, tau=tau), from=0, to=20,
n=20+1, type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#-------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1BNB(0:19, mu=mu, sigma=sigma, nu=nu, tau=tau)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#-------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1BNB(seq(0.1,.99,length=20),mu, sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#-------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1BNB(1000, mu=mu, sigma=sigma, nu=nu, tau=tau)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#-------------------------------------------------------------------------------

---

K-inflated Delaporte distributions for fitting a GAMLSS model

Description

The function KIDEL defines the K-inflated Delaporte distribution, a four parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIDEL, pKIDEL, qKIDEL and rKIDEL define the density, distribution function, quantile function and random generation for the K-inflated Delaporte, KIDEL(), distribution.

Usage

KIDEL(mu.link = "log", sigma.link = "log", nu.link = "logit",
       tau.link = "logit", kinf="K")

dKIDEL(x, mu = 1, sigma = 1, nu = 0.5, tau = 0.1, kinf=0, log = FALSE)

pKIDEL(q, mu = 1, sigma = 1, nu = 0.5, tau = 0.1, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

qKIDEL(p, mu = 1, sigma = 1, nu = 0.5, tau = 0.1, kinf=0, lower.tail = TRUE,
    log.p = FALSE, max.value = 10000)

rKIDEL(n, mu = 1, sigma = 1, nu = 0.5, tau = 0.1, kinf=0, max.value = 10000)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "logit" link as the default for the nu parameter
tau.link	Defines the tau.link, with "logit" link as the default for the tau parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of nu
tau	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
max.value	a constant, set to the default value of 10000 for how far the algorithm should look for q

Details

The definition for the K-inflated Delaporte distribution.

Value

The functions KIDEL return a gamlss.family object which can be used to fit K-inflated Delaporte distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIDEL

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the Delaporte distribution
KIDEL()
#--------------------------------------------------------------------------------

# generate zero inflated Delaporte distribution
gen.Kinf(family=DEL, kinf=0)

# generate random sample from zero inflated Delaporte distribution
x<-rinf0DEL(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the zero inflated Delaporte distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0DEL, data=data)
histDist(x, family=inf0DEL)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Delaporte distribution
gen.Kinf(family=DEL, kinf=1)

# generate random sample from one inflated Delaporte distribution
x<-rinf1DEL(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the one inflated Delaporte distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1DEL, data=data)
histDist(x, family=inf1DEL)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2; tau=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1DEL(x, mu=mu, sigma=sigma, nu=nu, tau=tau), from=0, to=20,
n=20+1, type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1DEL(0:19, mu=mu, sigma=sigma, nu=nu, tau=tau)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1DEL(seq(0.1,.99,length=20),mu, sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1DEL(1000, mu=mu, sigma=sigma, nu=nu, tau=tau)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray",main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Double Poisson distributions for fitting a GAMLSS model

Description

The function KIDPO defines the K-inflated Double Poisson distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIDPO, pKIDPO, qKIDPO and rKIDPO define the density, distribution function, quantile function and random generation for the K-inflated Double Poisson, KIDPO(), distribution.

Usage

KIDPO(mu.link = "log", sigma.link = "log", nu.link = "logit", kinf="K")

dKIDPO(x, mu = 1, sigma = 1, nu = 0.3, kinf=0 ,log = FALSE)

pKIDPO(q, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

qKIDPO(p, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

rKIDPO(n, mu = 1, sigma = 1, nu = 0.3, kinf=0)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "logit" link as the default for the nu parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Double Poisson distribution.

Value

The functions KIDPO return a gamlss.family object which can be used to fit K-inflated Double Poisson distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIDPO

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Double Poisson distribution
KIDPO()
#--------------------------------------------------------------------------------

# generate zero inflated Double Poisson distribution
gen.Kinf(family=DPO, kinf=0)

# generate random sample from zero inflated Double Poisson distribution
x<-rinf0DPO(1000,mu=1, sigma=.5, nu=.2)

# fit the zero inflated Double Poisson distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0DPO, data=data)
histDist(x, family=inf0DPO)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Double Poisson distribution
gen.Kinf(family=DPO, kinf=1)

# generate random sample from one inflated Double Poisson distribution
x<-rinf1DPO(1000,mu=1, sigma=.5, nu=.2)

# fit the one inflated Double Poisson distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1DPO, data=data)
histDist(x, family=inf1DPO)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1DPO(x, mu=mu, sigma=sigma, nu=nu), from=0, to=20,
n=20+1, type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1DPO(0:19, mu=mu, sigma=sigma, nu=nu)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1DPO(seq(0.1,.99,length=20),mu, sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1DPO(1000, mu=mu, sigma=sigma, nu=nu)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Geometric distributions for fitting a GAMLSS model

Description

The function KIGEOM defines the K-inflated Geometric distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIGEOM, pKIGEOM, qKIGEOM and rKIGEOM define the density, distribution function, quantile function and random generation for the K-inflated Geometric, KIGEOM(), distribution.

Usage

KIGEOM(mu.link = "log", sigma.link = "logit", kinf="K")

dKIGEOM(x, mu = 1, sigma = 0.1, kinf=0, log = FALSE)

pKIGEOM(q, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

qKIGEOM(p, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

rKIGEOM(n, mu = 1, sigma = 0.1, kinf=0)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "logit" link as the default for the sigma parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Geometric distribution.

Value

The functions KIGEOM return a gamlss.family object which can be used to fit K-inflated Geometric distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIGEOM

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Geometric distribution
KIGEOM()
#--------------------------------------------------------------------------------

# generate zero inflated Geometric distribution
gen.Kinf(family=GEOM, kinf=0)

# generate random sample from zero inflated Geometric distribution
x<-rinf0GEOM(1000,mu=1, sigma=.2)

# fit the zero inflated Geometric distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0GEOM, data=data)
histDist(x, family=inf0GEOM)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Geometric distribution
gen.Kinf(family=GEOM, kinf=1)

# generate random sample from one inflated Geometric distribution
x<-rinf1GEOM(1000,mu=1, sigma=.2)

# fit the one inflated Geometric distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1GEOM, data=data)
histDist(x, family=inf1GEOM)
## End(Not run)
#--------------------------------------------------------------------------------

mu=1; sigma=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1GEOM(x, mu=mu, sigma=sigma), from=0, to=20, n=20+1,
     type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1GEOM(0:19, mu=mu, sigma=sigma)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE,cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19),qinf1GEOM(seq(0.1,.99,length=20),mu,        sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1GEOM(1000, mu=mu, sigma=sigma)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Geometric original distributions for fitting a GAMLSS model

Description

The function KIGEOMo defines the K-inflated Geometric original distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIGEOMo, pKIGEOMo, qKIGEOMo and rKIGEOMo define the density, distribution function, quantile function and random generation for the K-inflated Geometric original, KIGEOMo(), distribution.

Usage

KIGEOMo(mu.link = "logit", sigma.link = "logit", kinf="K")

dKIGEOMo(x, mu = .1, sigma = 0.1, kinf=0, log = FALSE)

pKIGEOMo(q, mu = .1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

qKIGEOMo(p, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

rKIGEOMo(n, mu = 1, sigma = 0.1, kinf=0)

Arguments

mu.link	Defines the mu.link, with "logit" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "logit" link as the default for the sigma parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Geometric original distribution.

Value

The functions KIGEOMo return a gamlss.family object which can be used to fit K-inflated Geometric original distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIGEOMo

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Geometric original distribution
KIGEOMo()
#--------------------------------------------------------------------------------

# generate zero inflated Geometric original distribution
gen.Kinf(family=GEOMo, kinf=0)

# generate random sample from zero inflated Geometric original distribution
x<-rinf0GEOMo(1000,mu=.5, sigma=.2)

# fit the zero inflated Geometric original distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0GEOMo, data=data)
histDist(x, family=inf0GEOMo)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Geometric original distribution
gen.Kinf(family=GEOMo, kinf=1)

# generate random sample from one inflated Geometric original distribution
x<-rinf1GEOMo(1000,mu=.5, sigma=.2)

# fit the one inflated Geometric original distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1GEOMo, data=data)
histDist(x, family=inf1GEOMo)
## End(Not run)
#--------------------------------------------------------------------------------

mu=.3; sigma=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)
#plot the pdf using plot
plot(function(x) dinf1GEOMo(x, mu=mu, sigma=sigma), from=0, to=20, n=20+1,
     type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1GEOMo(0:19, mu=mu, sigma=sigma)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main=""      ,cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1GEOMo(seq(0.1,.99,length=20),mu, sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1GEOMo(1000, mu=mu, sigma=sigma)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Generalised Poisson distributions for fitting a GAMLSS model

Description

The function KIGPO defines the K-inflated Generalised Poisson distribution,a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIGPO, pKIGPO, qKIGPO and rKIGPO define the density, distribution function, quantile function and random generation for the K-inflated Generalised Poisson, KIGPO(), distribution.

Usage

KIGPO(mu.link = "log", sigma.link = "log", nu.link = "logit", kinf="K")

dKIGPO(x, mu = 1, sigma = 1, nu = 0.3, kinf=0 ,log = FALSE)

pKIGPO(q, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

qKIGPO(p, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

rKIGPO(n, mu = 1, sigma = 1, nu = 0.3, kinf=0)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "logit" link as the default for the nu parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Generalised Poisson distribution.

Value

The functions KIGPO return a gamlss.family object which can be used to fit K-inflated Generalised Poisson distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIGPO

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Generalised Poisson distribution
KIGPO()
#--------------------------------------------------------------------------------

# generate zero inflated Generalised Poisson distribution
gen.Kinf(family=GPO, kinf=0)

# generate random sample from zero inflated Generalised Poisson distribution
x<-rinf0GPO(1000,mu=1, sigma=.5, nu=.2)

# fit the zero inflated Generalised Poisson distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0GPO, data=data)
histDist(x, family=inf0GPO)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Generalised Poisson distribution
gen.Kinf(family=GPO, kinf=1)

# generate random sample from one inflated Generalised Poisson distribution
x<-rinf1GPO(1000,mu=1, sigma=.5, nu=.2)

# fit the one inflated Generalised Poisson distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1GPO, data=data)
histDist(x, family=inf1GPO)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1GPO(x, mu=mu, sigma=sigma, nu=nu), from=0, to=20,
n=20+1, type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1GPO(0:19, mu=mu, sigma=sigma, nu=nu)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1GPO(seq(0.1,.99,length=20),mu,        sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1GPO(1000, mu=mu, sigma=sigma, nu=nu)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray",main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Logarithmic distributions for fitting a GAMLSS model

Description

The function KILG defines the K-inflated Logarithmic distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().The functions dKILG, pKILG, qKILG and rKILG define the density, distribution function, quantile function and random generation for the K-inflated Logarithmic, KILG(), distribution.

Usage

KILG(mu.link = "logit", sigma.link = "logit", kinf="K")

dKILG(x, mu = .1, sigma = 0.1, kinf=0, log = FALSE)

pKILG(q, mu = .1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

qKILG(p, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

rKILG(n, mu = 1, sigma = 0.1, kinf=0)

Arguments

mu.link	Defines the mu.link, with "logit" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "logit" link as the default for the sigma parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Logarithmic distribution.

Value

The functions KILG return a gamlss.family object which can be used to fit K-inflated Logarithmic distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KILG

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Logarithmic distribution
KILG()
#--------------------------------------------------------------------------------

# generate zero inflated Logarithmic distribution
gen.Kinf(family=LG, kinf=0)

# generate random sample from zero inflated Logarithmic distribution
x<-rinf0LG(1000,mu=.1, sigma=.2)

# fit the zero inflated Logarithmic distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0LG, data=data)
histDist(x, family=inf0LG)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Logarithmic distribution
gen.Kinf(family=LG, kinf=1)

# generate random sample from one inflated Logarithmic distribution
x<-rinf1LG(1000,mu=.1, sigma=.2)

# fit the one inflated Logarithmic distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1LG, data=data)
histDist(x, family=inf1LG)
## End(Not run)
#--------------------------------------------------------------------------------

mu=.5; sigma=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1LG(x, mu=mu, sigma=sigma), from=1, to=20, n=20+1,
type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(1:19, c(0,pinf1LG(1:19, mu=mu, sigma=sigma)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1LG(seq(0.1,.99,length=20),mu, sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1LG(1000, mu=mu, sigma=sigma)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Negative Binomial Family distributions for fitting a GAMLSS model

Description

The function KINBF defines the K-inflated Negative Binomial Family distribution, a four parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKINBF, pKINBF, qKINBF and rKINBF define the density, distribution function, quantile function and random generation for the K-inflated Negative Binomial Family, KINBF(), distribution.

Usage

KINBF(mu.link = "log", sigma.link = "log", nu.link = "log",
    tau.link = "logit", kinf="K")

dKINBF(x, mu = 1, sigma = 1, nu = 2, tau = 0.1, kinf=0, log = FALSE)

pKINBF(q, mu = 1, sigma = 1, nu = 2, tau = 0.1, kinf=0, lower.tail = TRUE,
            log.p = FALSE)

qKINBF(p, mu = 1, sigma = 1, nu = 2, tau = 0.1, kinf=0, lower.tail = TRUE,
            log.p = FALSE)

rKINBF(n, mu = 1, sigma = 1, nu = 2, kinf=0, tau = 0.1)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "log" link as the default for the nu parameter
tau.link	Defines the tau.link, with "logit" link as the default for the tau parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of nu
tau	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Negative Binomial Family distribution.

Value

The functions KINBF return a gamlss.family object which can be used to fit K-inflated Negative Binomial Family distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KINBF

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Negative Binomial Family distribution
KINBF()
#--------------------------------------------------------------------------------

# generate zero inflated Negative Binomial Family distribution
gen.Kinf(family=NBF, kinf=0)

# generate random sample from zero inflated Negative Binomial Family distribution
x<-rinf0NBF(1000,mu=1, sigma=.5, nu=-.2, tau=.2)

# fit the zero inflated Negative Binomial Family distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0NBF, data=data)
histDist(x, family=inf0NBF)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Negative Binomial Family distribution
gen.Kinf(family=NBF, kinf=1)

# generate random sample from one inflated Negative Binomial Family distribution
x<-rinf1NBF(1000,mu=1, sigma=.5, nu=-.2, tau=.2)

# fit the one inflated Negative Binomial Family distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1NBF, data=data)
histDist(x, family=inf1NBF)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2; tau=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1NBF(x, mu=mu, sigma=sigma, nu=nu, tau=tau), from=0, to=20,
n=20+1, type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1NBF(0:19, mu=mu, sigma=sigma, nu=nu, tau=tau)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1NBF(seq(0.1,.99,length=20),mu,        sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1NBF(1000, mu=mu, sigma=sigma, nu=nu, tau=tau)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Negative Binomial distributions for fitting a GAMLSS model

Description

The function KINBI defines the K-inflated Negative Binomial distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKINBI, pKINBI, qKINBI and rKINBI define thedensity, distribution function, quantile function and random generation for the K-inflated Negative Binomial,KINBI(), distribution.

Usage

KINBI(mu.link = "log", sigma.link = "log", nu.link = "logit", kinf="K")

dKINBI(x, mu = 1, sigma = 1, nu = 0.3, kinf=0 ,log = FALSE)

pKINBI(q, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

qKINBI(p, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

rKINBI(n, mu = 1, sigma = 1, nu = 0.3, kinf=0)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "logit" link as the default for the nu parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Negative Binomial distribution.

Value

The functions KINBI return a gamlss.family object which can be used to fit K-inflated Negative Binomial distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KINBI

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Negative Binomial distribution
KINBI()
#--------------------------------------------------------------------------------

# generate zero inflated Negative Binomial distribution
gen.Kinf(family=NBI, kinf=0)

# generate random sample from zero inflated Negative Binomial distribution
x<-rinf0NBI(1000,mu=1, sigma=.5, nu=.2)

# fit the zero inflated Negative Binomial distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0NBI, data=data)
histDist(x, family=inf0NBI)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Negative Binomial distribution
gen.Kinf(family=NBI, kinf=1)

# generate random sample from one inflated Negative Binomial distribution
x<-rinf1NBI(1000,mu=1, sigma=.5, nu=.2)

# fit the one inflated Negative Binomial distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1NBI, data=data)
histDist(x, family=inf1NBI)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1NBI(x, mu=mu, sigma=sigma, nu=nu), from=0, to=20, n=20+1,
     type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1NBI(0:19, mu=mu, sigma=sigma, nu=nu)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE,
     cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1NBI(seq(0.1,.99,length=20),mu,        sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1NBI(1000, mu=mu, sigma=sigma, nu=nu)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Negative Binomial type II distributions for fitting a GAMLSS model

Description

The function KINBII defines the K-inflated Negative Binomial type II distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKINBII, pKINBII, qKINBII and rKINBII define the density, distribution function, quantile function and random generation for the K-inflated Negative Binomial type II, KINBII(), distribution.

Usage

KINBII(mu.link = "log", sigma.link = "log", nu.link = "logit", kinf="K")

dKINBII(x, mu = 1, sigma = 1, nu = 0.3, kinf=0 ,log = FALSE)

pKINBII(q, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

qKINBII(p, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

rKINBII(n, mu = 1, sigma = 1, nu = 0.3, kinf=0)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "logit" link as the default for the nu parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Negative Binomial type II distribution.

Value

The functions KINBII return a gamlss.family object which can be used to fit K-inflated Negative Binomial type II distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KINBII

Examples

#--------------------------------------------------------------------------------

# gives default links for the  Negative Binomial distribution  type II
KINBII()
#--------------------------------------------------------------------------------

# generate zero inflated Negative Binomial type II distribution
gen.Kinf(family=NBII, kinf=0)

# generate random sample from zero inflated Negative Binomial type II distribution
x<-rinf0NBII(1000, mu=1, sigma=.5, nu=.2)

# fit the zero inflated Negative Binomial type II distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0NBII, data=data)
histDist(x, family=inf0NBII)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Negative Binomial  type II distribution
gen.Kinf(family=NBII, kinf=1)

# generate random sample from one inflated Negative Binomial type II distribution
x<-rinf1NBII(1000,mu=1, sigma=.5, nu=.2)

# fit the one inflated Negative Binomial type II distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1NBII, data=data)
histDist(x, family=inf1NBII)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2; tau=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1NBII(x, mu=mu, sigma=sigma, nu=nu), from=0, to=20, n=20+1,
     type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1NBII(0:19, mu=mu, sigma=sigma, nu=nu)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1NBII(seq(0.1,.99,length=20),mu,       sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1NBII(1000, mu=mu, sigma=sigma, nu=nu)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Poisson Inverse Gaussian distributions for fitting a GAMLSS model

Description

The function KIPIG defines the K-inflated Poisson Inverse Gaussian distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIPIG, pKIPIG, qKIPIG and rKIPIG define the density, distribution function, quantile function and random generation for the K-inflated Poisson Inverse Gaussian, KIPIG(), distribution.

Usage

KIPIG(mu.link = "log", sigma.link = "log", nu.link = "logit", kinf="K")

dKIPIG(x, mu = 1, sigma = 1, nu = 0.3, kinf=0, log = FALSE)

pKIPIG(q, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

qKIPIG(p, mu = 1, sigma = 1, nu = 0.3,  kinf=0, lower.tail = TRUE,
    log.p = FALSE, max.value = 10000)

rKIPIG(n, mu = 1, sigma = 1, nu = 0.3, kinf=0, max.value = 10000)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "logit" link as the default for the nu parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
max.value	a constant, set to the default value of 10000 for how far the algorithm should look for q

Details

The definition for the K-inflated Poisson Inverse Gaussian distribution.

Value

The functions KIPIG return a gamlss.family object which can be used to fit K-inflated Poisson Inverse Gaussian distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIPIG

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Poisson Inverse Gaussian distribution
KIPIG()
#--------------------------------------------------------------------------------

# generate zero inflated Poisson Inverse Gaussian distribution
gen.Kinf(family=PIG, kinf=0)

# generate random sample from zero inflated Poisson Inverse Gaussian distribution
x<-rinf0PIG(1000,mu=1, sigma=.5, nu=.2)

# fit the zero inflated Poisson Inverse Gaussian distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0PIG, data=data)
histDist(x, family=inf0PIG)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Poisson Inverse Gaussian distribution
gen.Kinf(family=PIG, kinf=1)

# generate random sample from one inflated Poisson Inverse Gaussian distribution
x<-rinf1PIG(1000,mu=1, sigma=.5, nu=.2)

# fit the one inflated Poisson Inverse Gaussian distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1PIG, data=data)
histDist(x, family=inf1PIG)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1PIG(x, mu=mu, sigma=sigma, nu=nu), from=0, to=20, n=20+1,
     type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1PIG(0:19, mu=mu, sigma=sigma, nu=nu)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1PIG(seq(0.1,.99,length=20),mu,        sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1PIG(1000, mu=mu, sigma=sigma, nu=nu)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Poisson distributions for fitting a GAMLSS model

Description

The function KIPO defines the K-inflated Poisson distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIPO, pKIPO, qKIPO and rKIPO define the density, distribution function, quantile function and random generation for the K-inflated Poisson, KIPO(), distribution.

Usage

KIPO(mu.link = "log", sigma.link = "logit", kinf="K")

dKIPO(x, mu = 1, sigma = 0.1, kinf=0, log = FALSE)

pKIPO(q, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

qKIPO(p, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

rKIPO(n, mu = 1, sigma = 0.1, kinf=0)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "logit" link as the default for the sigma parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Poisson distribution.

Value

The functions KIPO return a gamlss.family object which can be used to fit K-inflated Poisson distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIPO

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Poisson distribution  type II
KIPO()
#--------------------------------------------------------------------------------

# generate zero inflated Poisson distribution
gen.Kinf(family=PO, kinf=0)

# generate random sample from zero inflated Poisson distribution
x<-rinf0PO(1000,mu=1, sigma=.1)

# fit the zero inflated Poisson distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0PO, data=data)
histDist(x, family=inf0PO)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Poisson distribution
gen.Kinf(family=PO, kinf=1)

# generate random sample from one inflated Poisson distribution
x<-rinf1PO(1000,mu=1, sigma=.1)

# fit the one inflated Poisson distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1PO, data=data)
histDist(x, family=inf1PO)
## End(Not run)
#--------------------------------------------------------------------------------

mu=1; sigma=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1PO(x, mu=mu, sigma=sigma), from=0, to=20, n=20+1,
     type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1PO(0:19, mu=mu, sigma=sigma)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1PO(seq(0.1,.99,length=20),mu,         sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1PO(1000, mu=mu, sigma=sigma)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated sichel distributions for fitting a GAMLSS model

Description

The function KISI defines the K-inflated sichel distribution, a four parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKISI, pKISI, qKISI and rKISI define the density, distribution function, quantile function and random generation for the K-inflated sichel, KISI(), distribution.

Usage

KISI(mu.link = "log", sigma.link = "log", nu.link = "identity",
      tau.link = "logit", kinf="K")

dKISI(x, mu = 1, sigma = 1, nu = -0.5, tau = 0.1, kinf=0, log = FALSE)

pKISI(q, mu = 1, sigma = 1, nu = -0.5, tau = 0.1, kinf=0, lower.tail = TRUE,
log.p = FALSE)

qKISI(p, mu = 1, sigma = 1, nu = -0.5, tau = 0.1,  kinf=0, lower.tail = TRUE,
log.p = FALSE, max.value = 10000)

rKISI(n, mu = 1, sigma = 1, nu = -0.5, tau = 0.1,  kinf=0, max.value = 10000)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "identity" link as the default for the nu parameter
tau.link	Defines the tau.link, with "logit" link as the default for the tau parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive mu
sigma	vector of positive despersion parameter
nu	vector of nu
tau	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
max.value	a constant, set to the default value of 10000 for how far the algorithm should look for q

Details

The definition for the K-inflated sichel distribution.

Value

The functions KISI return a gamlss.family object which can be used to fit K-inflated sichel distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KISICHEL

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Sichel distribution
KISI()
#--------------------------------------------------------------------------------

# generate zero inflated sichel distribution
gen.Kinf(family=SI, kinf=0)

# generate random sample from zero inflated sichel distribution
x<-rinf0SI(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the zero inflated sichel distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0SI, data=data)
histDist(x, family=inf0SI)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated sichel distribution
gen.Kinf(family=SI, kinf=1)

# generate random sample from one inflated sichel distribution
x<-rinf1SI(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the one inflated sichel distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1SI, data=data)
histDist(x, family=inf1SI)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2; tau=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1SI(x, mu=mu, sigma=sigma, nu=nu, tau=tau), from=0, to=20,
n=20+1, type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1SI(0:19, mu=mu, sigma=sigma, nu=nu, tau=tau)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1SI(seq(0.1,.99,length=20),mu,         sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1SI(1000, mu=mu, sigma=sigma, nu=nu, tau=tau)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray",main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated sichel distributions for fitting a GAMLSS model

Description

The function KISICHEL defines the K-inflated sichel distribution, a four parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKISICHEL, pKISICHEL, qKISICHEL and rKISICHEL define the density, distribution function, quantile function and random generation for the K-inflated sichel, KISICHEL(), distribution.

Usage

KISICHEL(mu.link = "log", sigma.link = "log", nu.link = "identity",
          tau.link = "logit", kinf="K")

dKISICHEL(x, mu = 1, sigma = 1, nu = -0.5, tau = 0.1, kinf=0, log = FALSE)

pKISICHEL(q, mu = 1, sigma = 1, nu = -0.5, tau = 0.1, kinf=0, lower.tail = TRUE,
log.p = FALSE)

qKISICHEL(p, mu = 1, sigma = 1, nu = -0.5, tau = 0.1,  kinf=0, lower.tail = TRUE,
log.p = FALSE, max.value = 10000)

rKISICHEL(n, mu = 1, sigma = 1, nu = -0.5, tau = 0.1, kinf = 0,
                 max.value = 10000)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "identity" link as the default for the nu parameter
tau.link	Defines the tau.link, with "logit" link as the default for the tau parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of nu
tau	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
max.value	a constant, set to the default value of 10000 for how far the algorithm should look for q

Details

The definition for the K-inflated sichel distribution.

Value

The functions KISICHEL return a gamlss.family object which can be used to fit K-inflated sichel distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KISICHEL

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Sichel distribution
KISICHEL()
#--------------------------------------------------------------------------------

# generate zero inflated sichel distribution
gen.Kinf(family=SICHEL, kinf=0)

# generate random sample from zero inflated sichel distribution
x<-rinf0SICHEL(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the zero inflated sichel distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0SICHEL, data=data)
histDist(x, family=inf0SICHEL)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated sichel distribution
gen.Kinf(family=SICHEL, kinf=1)

# generate random sample from one inflated sichel distribution
x<-rinf1SICHEL(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the one inflated sichel distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1SICHEL, data=data)
histDist(x, family=inf1SICHEL)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2; tau=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1SICHEL(x, mu=mu, sigma=sigma, nu=nu, tau=tau),
from=0, to=20, n=20+1, type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1SICHEL(0:19, mu=mu, sigma=sigma, nu=nu, tau=tau)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1SICHEL(seq(0.1,.99,length=20),
     mu, sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1SICHEL(1000, mu=mu, sigma=sigma, nu=nu, tau=tau)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray",main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

---

K-inflated Waring distributions for fitting a GAMLSS model

Description

The function KIWARING defines the K-inflated Waring distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIWARING, pKIWARING, qKIWARING and rKIWARING define the density, distribution function, quantile function and random generation for the K-inflated Waring, KIWARING(), distribution.

Usage

KIWARING(mu.link = "log", sigma.link = "log", nu.link = "logit", kinf="K")

dKIWARING(x, mu = 1, sigma = 1, nu = 0.3, kinf=0 ,log = FALSE)

pKIWARING(q, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

qKIWARING(p, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

rKIWARING(n, mu = 1, sigma = 1, nu = 0.3, kinf=0)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "logit" link as the default for the nu parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
log, log.p	logical; if TRUE, probabilities p are given as log(p)
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The definition for the K-inflated Waring distribution.

Value

The functions KIWARING return a gamlss.family object which can be used to fit K-inflated Waring distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[email protected]>, Mikis Stasinopoulos <[email protected]>

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),Appl. Statist.,54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KIWARING

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Waring distribution
KIWARING()
#--------------------------------------------------------------------------------

# generate zero inflated Waring distribution
gen.Kinf(family=WARING, kinf=0)

# generate random sample from zero inflated Waring distribution
x<-rinf0WARING(1000,mu=1, sigma=.5, nu=.2)

# fit the zero inflated Waring distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0WARING, data=data)
histDist(x, family=inf0WARING)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Waring distribution
gen.Kinf(family=WARING, kinf=1)

# generate random sample from one inflated Waring distribution
x<-rinf1WARING(1000,mu=1, sigma=.5, nu=.2)

# fit the one inflated Waring distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1WARING, data=data)
histDist(x, family=inf1WARING)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1WARING(x, mu=mu, sigma=sigma, nu=nu), from=0, to=20,
n=20+1, type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1WARING(0:19, mu=mu, sigma=sigma, nu=nu)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE, cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1WARING(seq(0.1,.99,length=20),mu, sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1WARING(1000, mu=mu, sigma=sigma, nu=nu)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

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