Package 'poistweedie' reference manual

Title:	Poisson-Tweedie Exponential Family Models
Description:	Simulation of models Poisson-Tweedie.
Authors:	David Pechel Cactcha, Laure Pauline Fotso and Celestin C Kokonendji
Maintainer:	David Pechel Cactcha <[email protected]>
License:	GPL (>= 2)
Version:	1.0.2
Built:	2024-12-01 08:34:55 UTC
Source:	CRAN

The individual probabilities of Y when Y follows a Poisson-Tweedie Distributions

Description

Let X be a non-negative random variable following $\mathcal{T}_{P}(\theta , \lambda)$ . If a discrete random variable Y is such that the conditional distribution of Y given X is Poisson with mean X, then the EDM generated by the distribution of Y is of the Poisson-Tweedie class. For $p>=1$ individual probabilities of $Y\sim\mathcal{P\mathcal{T}_{P}(\theta ,\lambda )}$ when Y follows a Poisson-Tweedie Distributions are: $Pr(Y=y)=\int_{0}^{\infty}\frac{e^{-x}x^{y}}{y!}\mathcal{T}_{P}(\theta , \lambda)d(x), y=0,1,$ .
For p = 1, it is a Neyman type A distribution; for $1<p<2$ , then Poisson-compound Poisson distribution is obtained; for p = 2,the Poisson-Tweedie model $PT_{2}\left(\mu,\lambda\right)$ correspond to the negative binomiale law $BN\left( \lambda,\frac{1}{1+\mu}\right)$ ; and, for p = 3, it is the Sichel or Poisson-inverse Gaussian distribution (e.g. Willmot, 1987). Also, when $p\longrightarrow\infty$ , $\lambda=\frac{\mu\times\left( 1-\theta_{0}\right) }{1+\mu}$ and the $\lambda=\mu\simeq-\theta_{0}$ , the Poisson-Tweedie model $PT_{p}\left( \mu,\lambda\right)$ correspond to the poisson law $P_{y}\left( \lambda^{2}\right)$ .

Usage

dpoistweedie(y, p, mu, lambda, theta0, log)
       densitept1(p, n, mu, lambda, theta0)
       densitept2(p, n, mu, lambda, theta0)
       dpt1(p, n, mu, lambda, theta0)
       dpt1Log(p, n, mu, lambda, theta0)
       dpt2(p, n, mu, lambda, theta0)
       dpt2Log(p, n, mu, lambda, theta0)
       dptp(p, n, mu, lambda, theta0)
       dptpLog(p, n, mu, lambda, theta0)
       gam1.1(y, lambda)
       gam1.2(y, lambda)
       imfx0(x0,p,mu,theta0)
       moyennePT(p,omega,theta0)
       omega(p,mu,theta0)
       testOmegaPT(p,n)

dpoistweedie(y, p, mu, lambda, theta0, log)
       densitept1(p, n, mu, lambda, theta0)
       densitept2(p, n, mu, lambda, theta0)
       dpt1(p, n, mu, lambda, theta0)
       dpt1Log(p, n, mu, lambda, theta0)
       dpt2(p, n, mu, lambda, theta0)
       dpt2Log(p, n, mu, lambda, theta0)
       dptp(p, n, mu, lambda, theta0)
       dptpLog(p, n, mu, lambda, theta0)
       gam1.1(y, lambda)
       gam1.2(y, lambda)
       imfx0(x0,p,mu,theta0)
       moyennePT(p,omega,theta0)
       omega(p,mu,theta0)
       testOmegaPT(p,n)

Arguments

`y`	vector of (non-negative integer) quantiles $Y=(y1,y2,...,yn) \ where \ \ yi i=1,2,...,n$ are the integer.
`p`	is a real index related to a precise model $p>=1$ .
`n`	non-negative integer (length of y)
`x0`	is a real index
`mu`	the mean $\mu\in{R}^{+}$ , .
`omega`	is a real index. $\omega\in{R}$
`lambda`	the dispersion parameter $\lambda\in{R},\lambda>0$ .
`theta0`	the canonical parameter $\theta_{0}\in{R}^{-}$ .
`log`	logical; if TRUE, probabilities y are given as log(y).

Details

The Poisson-Tweedie distributions arethe EDMs with a variance of the form $V_{p}^{\mathcal{PT}}\left( \mu\right) =\mu+\mu^{p}\exp\left\{ \left(2-p\right) \Phi_{p}\left( \mu\right) \right\} ,\mu>0$ , where $\Phi_{p}\left( \mu\right)$ a generally implicit, denotes the inverse of the increansing function $\omega\longrightarrow\frac{d\left\{ \ln IE\left( e^{wy}\right) \right\}}{dw}$ . omega(p,mu,theta0) is a function whose permit to determine the value of w.

Value

density (dpoistweedie),for the given Poisson-Tweedie distribution with parameters

Author(s)

Cactha David Pechel, Laure Pauline Fotso and Celestin C Kokonendji Maintainer: Cactha David Pechel ( <[email protected]>)

References

Dunn, Peter K and Smyth, Gordon K (To appear). Series evaluation of Tweedie exponential dispersion model densities Statistics and Computing.

Dunn, Peter K and Smyth, Gordon K (2001). Tweedie family densities: methods of evaluation. Proceedings of the 16th International Workshop on Statistical Modelling, Odense, Denmark, 2–6 July

Hougaard, P., Lee, M-L.T. and Whitmore, G.A. (1997). Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes, Biometrics 53, 1225–1238

Jorgensen, B. (1987). Exponential dispersion models. Journal of the Royal Statistical Society, B, 49, 127–162.

Kokonendji, C.C., Demeetrio, C.G.B. and Dossou-Gbete, S. (2004). Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Demetrio classes. SORT: Statistics and Operations Research Transactions 28 (2), 201–214.

Examples

   
## dpoistweedie(y, power, mu,lambda,theta0,log = FALSE)
## Plot dpois() and dpoistweedie() with  log=FALSE
layout(matrix(1 :1, 1, 1))
layout.show(2) 
power <- exp(10) 
mu <-10
lambda <- 10
theta0<--10
lambda1<-100
y <- 0:200
## plot  dpoistweedie function with log = FALSE
d1<-dpoistweedie(y,power,mu,lambda,theta0,log = FALSE)
d2<-dpois(y,lambda1,log=FALSE)
erreure<-d1-d2
plot (y,d1,col='blue', type='h',xlab="y 
   avec  y=0:200,  power=exp(30),mu=10, lambda=10,
   theta0=-10,  lambda1=100", ylab="densite P(100)",
   main = "dpoistweedie(*,col='blue' log=FALSE)
   et dpois(*,col='red' log=FALSE)")
lines(y,d2,type ="p",col='red',lwd=2)
sum(abs(erreure))



## Plot dnbinom() and dpoistweedie()
layout(matrix(1 :1, 1, 1))
layout.show(2) 
power<-2 
mu<-10
lambda <- 1
theta0<-0
prob<-1-(mu/(1+mu))
y <- seq(0,50, by =3)
## plot a dpoistweedie function with log=FALSE
d1<-dpoistweedie(y,power,mu,lambda,theta0,log=FALSE)
d2<-dnbinom(y,lambda,prob, log=FALSE)
erreure<-d1-d2
plot (y,d1,col='blue', type='h',xlab="y 
   avec  y=seq(0,50,by=3),  power=2,mu=10, 
   lambda=1, thetao=0", ylab="densite NB(1,1/11)"
   ,main = "dnpoistweedie(*,col='blue' log=FALSE)
   et dnbinom(*,col='red' log=FALSE)")
lines(y,d2,type ="p",col='red',lwd=2)
abs(erreure)
 ## dpoistweedie(y, power, mu,lambda,theta0,log = FALSE)
## Plot dpois() and dpoistweedie() with  log=FALSE
layout(matrix(1 :1, 1, 1))
layout.show(2) 
power <- exp(10) 
mu <-10
lambda <- 10
theta0<--10
lambda1<-100
y <- 0:200
## plot  dpoistweedie function with log = FALSE
d1<-dpoistweedie(y,power,mu,lambda,theta0,log = FALSE)
d2<-dpois(y,lambda1,log=FALSE)
erreure<-d1-d2
plot (y,d1,col='blue', type='h',xlab="y 
   avec  y=0:200,  power=exp(30),mu=10, lambda=10,
   theta0=-10,  lambda1=100", ylab="densite P(100)",
   main = "dpoistweedie(*,col='blue' log=FALSE)
   et dpois(*,col='red' log=FALSE)")
lines(y,d2,type ="p",col='red',lwd=2)
sum(abs(erreure))



## Plot dnbinom() and dpoistweedie()
layout(matrix(1 :1, 1, 1))
layout.show(2) 
power<-2 
mu<-10
lambda <- 1
theta0<-0
prob<-1-(mu/(1+mu))
y <- seq(0,50, by =3)
## plot a dpoistweedie function with log=FALSE
d1<-dpoistweedie(y,power,mu,lambda,theta0,log=FALSE)
d2<-dnbinom(y,lambda,prob, log=FALSE)
erreure<-d1-d2
plot (y,d1,col='blue', type='h',xlab="y 
   avec  y=seq(0,50,by=3),  power=2,mu=10, 
   lambda=1, thetao=0", ylab="densite NB(1,1/11)"
   ,main = "dnpoistweedie(*,col='blue' log=FALSE)
   et dnbinom(*,col='red' log=FALSE)")
lines(y,d2,type ="p",col='red',lwd=2)
abs(erreure)

Poisson-Tweedie (Some discrete exponential dispersion models)

Description

Density, Log of density, variance for the Poisson-Tweedie family of distributions

Usage

poistweedie(x, n, p, mu, lambda, theta0, lower.tail = TRUE, log.p = FALSE, 
    fonction = "PROBABILITE")
poisson(x, n, p, lambda1, lower.tail = TRUE, log.p = FALSE, 
    fonction = "PROBABILITE")
nbinomiale(x, n, p, lambda1, p1, lower.tail = TRUE, log.p = FALSE, 
    fonction = "PROBABILITE")

poistweedie(x, n, p, mu, lambda, theta0, lower.tail = TRUE, log.p = FALSE, 
    fonction = "PROBABILITE")
poisson(x, n, p, lambda1, lower.tail = TRUE, log.p = FALSE, 
    fonction = "PROBABILITE")
nbinomiale(x, n, p, lambda1, p1, lower.tail = TRUE, log.p = FALSE, 
    fonction = "PROBABILITE")

Arguments

`x`	vector of (non-negative integer) quantiles.
`p`	is a real index related to a precise model.
`p1`	is a real index related to a precise model.
`n`	non-negative integer
`mu`	the mean.
`lambda`	the dispersion parameter.
`lambda1`	the dispersion parameter.
`theta0`	the canonical parameter.
`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].
`fonction`	is a string

Details

Density, Log of density, variance for the Poisson-Tweedie family of distributions

Author(s)

Cactha David Pechel, Laure Pauline Fotso and Celestin C Kokonendji Maintainer: Cactha David Pechel ( <[email protected]>)

Examples

## poistweedie(x, n, p, mu, lambda, theta0, lower.tail = TRUE, 
##             log.p = FALSE, fonction = "PROBABILITE")
x <- 0:200
p <- 1.5
mu <-10     
lambda <- 10
theta0<--10
d1<-poistweedie(x, n, p, mu, lambda, theta0, lower.tail = TRUE,
log.p = FALSE, fonction = "PROBABILITE")
## poistweedie(x, n, p, mu, lambda, theta0, lower.tail = TRUE, 
##             log.p = FALSE, fonction = "PROBABILITE")
x <- 0:200
p <- 1.5
mu <-10     
lambda <- 10
theta0<--10
d1<-poistweedie(x, n, p, mu, lambda, theta0, lower.tail = TRUE,
log.p = FALSE, fonction = "PROBABILITE")

Distribution function for the Poisson-Tweedie family

Description

Distribution function, for the Poisson-Tweedie family of distributions

Usage

ppoistweedie(q, p, mu, lambda, theta0, lower.tail, log.p)ppoistweedie(q, p, mu, lambda, theta0, lower.tail, log.p)

Arguments

`q`	vector of quantiles.
`p`	is a real index related to a precise model.
`mu`	the mean.
`lambda`	the dispersion parameter.
`theta0`	the canonical parameter.
`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 Poisson-Tweedie family of distributions belong to the class of exponential dispersion models (EDMs), famous for their role in generalized linear models.

Value

probability (ppoistweedie), for the given Poisson-Tweedie distribution with parameters

Author(s)

Cactha David Pechel, Laure Pauline Fotso and Celestin C Kokonendji Maintainer: Cactha David Pechel ( <[email protected]>)

Examples

   
## function ppoistweedie(q, power, mu,lambda,theta0,
## lower.tail = TRUE, log.p = FALSE)
## Plot ppois() et ppoistweedie() avec log.p=FALSE
layout(matrix(1 :1, 1, 1))
layout.show(1)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
power<-exp(30) 
mu<-5
lambda <- 5
theta0<--5
prob<-1-(mu/(1+mu))
lambda1<-lambda^2
q <- 0:100
## function ppoistweedie function with log=FALSE
d1<-ppoistweedie(q,power,mu,lambda,theta0,lower.tail=TRUE,log.p=FALSE)
d2<-ppois(q,lambda1,lower.tail=TRUE,log.p=FALSE)
erreure<- d1-d2
plot (q,d1,col='blue', type='h',xlab="q    
 avec  q=0:100,  power=exp(30),mu=5, lambda=5, 
 theta0=-5, lambda1=25", ylab="fonction de 
 repartition P(25)",main = "ppoistweedie(*,col='blue' log=FALSE)
 et ppois(*,col='red' log=FALSE)")
lines(q,d2,type ="p",col='red',lwd=2)
sum(abs(erreure))


## function ppoistweedie(q, power, mu,lambda,theta0,
## lower.tail = TRUE, log.p = FALSE)
## Plot ppois() et ppoistweedie() avec log.p=FALSE
layout(matrix(1 :1, 1, 1))
layout.show(1)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
power<-exp(30) 
mu<-5
lambda <- 5
theta0<--5
prob<-1-(mu/(1+mu))
lambda1<-lambda^2
q <- 0:100
## function ppoistweedie function with log=FALSE
d1<-ppoistweedie(q,power,mu,lambda,theta0,lower.tail=TRUE,log.p=FALSE)
d2<-ppois(q,lambda1,lower.tail=TRUE,log.p=FALSE)
erreure<- d1-d2
plot (q,d1,col='blue', type='h',xlab="q    
 avec  q=0:100,  power=exp(30),mu=5, lambda=5, 
 theta0=-5, lambda1=25", ylab="fonction de 
 repartition P(25)",main = "ppoistweedie(*,col='blue' log=FALSE)
 et ppois(*,col='red' log=FALSE)")
lines(q,d2,type ="p",col='red',lwd=2)
sum(abs(erreure))

Quantile function for the Poisson-Tweedie family of distributions

Description

Quantile function for the Poisson-Tweedie family of distributions

Usage

qpoistweedie(p1, p, mu, lambda, theta0, lower.tail, log.p)qpoistweedie(p1, p, mu, lambda, theta0, lower.tail, log.p)

Arguments

`p1`	vector of probabilities.
`p`	is a real index related to a precise model.
`mu`	the mean.
`lambda`	the dispersion parameter.
`theta0`	the canonical parameter.
`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 Poisson-Tweedie family of distributions belong to the class of exponential dispersion models (EDMs), famous for their role in generalized linear models. T

Value

quantile (qpoistweedie) for the given Poisson-Tweedie distribution with parameters

Author(s)

Cactha David Pechel, Laure Pauline Fotso and Celestin C Kokonendji Maintainer: Cactha David Pechel ( <[email protected]>)

Examples

   
## function qpoistweedie(p, power, mu,lambda,theta0,
## lower.tail = TRUE, log.p = FALSE)
## Plot qpois() and qpoistweedie() with log.p=FALSE
layout(matrix(1 :1, 1, 1))
layout.show(1) 
power<-exp(30) 
mu<-10
lambda <- 10
theta0<--10
prob<-1-(mu/(1+mu))
lambda1<-100
p <- runif(50)
p
## plot of qpoistweedie function with log=FALSE
d1<-ppoistweedie(p,power,mu,lambda,theta0,lower.tail=TRUE,log.p=FALSE)
d2<-ppois(p,lambda1,lower.tail=TRUE,log.p=FALSE)
erreure<- d1-d2
plot (p,d1,col='blue', type='h',xlab="p 
   avec  p=runif(50),  power=exp(30),mu=10, lambda=10, 
   theta0=-10, lambda1=100, lower.tail=TRUE", 
   ylab="quantile function P(100)",main = 
   "qpoistweedie(*,col='blue' log.p=FALSE)
   et qpois(*,col='red' log.p=FALSE)")
lines(p,d2,type ="p",col='red',lwd=2)
sum(abs(erreure))

 ## function qpoistweedie(p, power, mu,lambda,theta0,
## lower.tail = TRUE, log.p = FALSE)
## Plot qpois() and qpoistweedie() with log.p=FALSE
layout(matrix(1 :1, 1, 1))
layout.show(1) 
power<-exp(30) 
mu<-10
lambda <- 10
theta0<--10
prob<-1-(mu/(1+mu))
lambda1<-100
p <- runif(50)
p
## plot of qpoistweedie function with log=FALSE
d1<-ppoistweedie(p,power,mu,lambda,theta0,lower.tail=TRUE,log.p=FALSE)
d2<-ppois(p,lambda1,lower.tail=TRUE,log.p=FALSE)
erreure<- d1-d2
plot (p,d1,col='blue', type='h',xlab="p 
   avec  p=runif(50),  power=exp(30),mu=10, lambda=10, 
   theta0=-10, lambda1=100, lower.tail=TRUE", 
   ylab="quantile function P(100)",main = 
   "qpoistweedie(*,col='blue' log.p=FALSE)
   et qpois(*,col='red' log.p=FALSE)")
lines(p,d2,type ="p",col='red',lwd=2)
sum(abs(erreure))

Random generation for the Poisson-Tweedie family of distributions

Description

Random generation for the Poisson-Tweedie family of distributions

Usage

rpoistweedie(n, p, mu, lambda, theta0)
rpoistweedie(n, p, mu, lambda, theta0)

Arguments

`n`	number of random values to return.
`p`	vector of probabilities.
`mu`	the mean.
`lambda`	the dispersion parameter.
`theta0`	the canonical parameter.

Details

The Poisson-Tweedie family of distributions belong to the class of exponential dispersion models (EDMs), famous for their role in generalized linear models.

Value

random sample (rpoistweedie) for the given Poisson-Tweedie distribution with parameters

Author(s)

Cactha David Pechel, Laure Pauline Fotso and Celestin C Kokonendji Maintainer: Cactha David Pechel ( <[email protected]>)

Examples

   
## --------------- function rpoistweedie()---------------- ##
layout(matrix(2 :1, 2,1))
layout.show(2) 
power<-exp(30) 
mu<-10
lambda <- 10
theta0<--10
prob<-1-(mu/(1+mu))
lambda1<-100
n<-10
set.seed(123)
x1<-rpoistweedie(n,power,mu,lambda,theta0)
set.seed(123)
x2<-rpois(n,lambda1)
hist(x1, xlim = c(min(x1),max(x1)), probability = FALSE,
  col ='blue',xlab="modalit\'{e}s: x1",ylab="effectifs ",
  nclass = max(x1) - min(x1),main="Histogramme de x1 
 (lambda=100, n=10)")
hist(x2, xlim = c(min(x2),max(x2)), probability = FALSE, 
  col ='blue',xlab="modalit\'{e}s: x2 ",ylab="effectifs ",
  nclass = max(x2) - min(x2),main="Histogramme de x2 
  (lambda1=100, n=10)")
sum(x2-x1)



 






 ## --------------- function rpoistweedie()---------------- ##
layout(matrix(2 :1, 2,1))
layout.show(2) 
power<-exp(30) 
mu<-10
lambda <- 10
theta0<--10
prob<-1-(mu/(1+mu))
lambda1<-100
n<-10
set.seed(123)
x1<-rpoistweedie(n,power,mu,lambda,theta0)
set.seed(123)
x2<-rpois(n,lambda1)
hist(x1, xlim = c(min(x1),max(x1)), probability = FALSE,
  col ='blue',xlab="modalit\'{e}s: x1",ylab="effectifs ",
  nclass = max(x1) - min(x1),main="Histogramme de x1 
 (lambda=100, n=10)")
hist(x2, xlim = c(min(x2),max(x2)), probability = FALSE, 
  col ='blue',xlab="modalit\'{e}s: x2 ",ylab="effectifs ",
  nclass = max(x2) - min(x2),main="Histogramme de x2 
  (lambda1=100, n=10)")
sum(x2-x1)

variance for the Poisson-Tweedie family of distributions

Description

Variance for the Poisson-Tweedie family of distributions

Usage

varpt(mu, p,  theta0)

varpt(mu, p,  theta0)

Arguments

`p`	is a real index related to a precise model.
`mu`	the mean.
`theta0`	the canonical parameter.

Details

variance for the Poisson-Tweedie family of distributions

Author(s)

Cactha David Pechel, Laure Pauline Fotso and Celestin C Kokonendji Maintainer: Cactha David Pechel ( <[email protected]>)

Examples

## plot of variance
layout(matrix(1:1,1,1))
layout.show(1)
mu <- seq(0.001,6,l=100)
var <-varpt(mu,p=5000,theta0=-150)
plot(mu, var, type = "l", col = "green", lwd=1,main="variance(p,mu,theta0=-150)")
grid(nx=1,ny=1, lty=1,lwd=2)
lines(mu,varpt(mu,p=1,theta0=-150), type = "l", col = "blue", lwd=1)
lines(mu,varpt(mu,p=2,theta0=-150), type = "l", col = "black", lwd=1)
lines(mu,varpt(mu,p=1.5,theta0=-150), type = "l", col = "yellow", lwd=1)
lines(mu,varpt(mu,p=2.5,theta0=-150), type = "l", col = "cyan", lwd=1)
lines(mu,varpt(mu,p=3,theta0=-150), type = "l", col = "magenta", lwd=1)
segments(4,2.5,4.5,2.5,col="blue" )
  text(5,2.5,"p=1",cex=0.8)
segments(4,2,4.5,2,col="yellow" )
  text(5,2,"1.5",cex=0.8)
segments(4,1.5,4.5,1.5,col= "black")
  text(5, 1.5,"p=2",cex=0.8)
segments(4,1,4.5,1,col="cyan" )
  text(5, 1,"p=2.5" ,cex=0.8)
segments(4,0.5,4.5,0.5,col="magenta" )
  text(5, 0.5,"p=3" ,cex=0.8) 
segments(4,0,4.5,0,col= "green" )
  text(5, 0,"p=5000",cex=0.8)  
## plot of variance
layout(matrix(1:1,1,1))
layout.show(1)
mu <- seq(0.001,6,l=100)
var <-varpt(mu,p=5000,theta0=-150)
plot(mu, var, type = "l", col = "green", lwd=1,main="variance(p,mu,theta0=-150)")
grid(nx=1,ny=1, lty=1,lwd=2)
lines(mu,varpt(mu,p=1,theta0=-150), type = "l", col = "blue", lwd=1)
lines(mu,varpt(mu,p=2,theta0=-150), type = "l", col = "black", lwd=1)
lines(mu,varpt(mu,p=1.5,theta0=-150), type = "l", col = "yellow", lwd=1)
lines(mu,varpt(mu,p=2.5,theta0=-150), type = "l", col = "cyan", lwd=1)
lines(mu,varpt(mu,p=3,theta0=-150), type = "l", col = "magenta", lwd=1)
segments(4,2.5,4.5,2.5,col="blue" )
  text(5,2.5,"p=1",cex=0.8)
segments(4,2,4.5,2,col="yellow" )
  text(5,2,"1.5",cex=0.8)
segments(4,1.5,4.5,1.5,col= "black")
  text(5, 1.5,"p=2",cex=0.8)
segments(4,1,4.5,1,col="cyan" )
  text(5, 1,"p=2.5" ,cex=0.8)
segments(4,0.5,4.5,0.5,col="magenta" )
  text(5, 0.5,"p=3" ,cex=0.8) 
segments(4,0,4.5,0,col= "green" )
  text(5, 0,"p=5000",cex=0.8)

Package 'poistweedie'

Help Index

The individual probabilities of Y when Y follows a Poisson-Tweedie Distributions

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Poisson-Tweedie (Some discrete exponential dispersion models)

Description

Usage

Arguments

Details

Author(s)

See Also

Examples

Distribution function for the Poisson-Tweedie family

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Quantile function for the Poisson-Tweedie family of distributions

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Random generation for the Poisson-Tweedie family of distributions

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

variance for the Poisson-Tweedie family of distributions

Description

Usage

Arguments

Details

Author(s)

See Also

Examples