| Title: | Multisection Composite Distributions |
|---|---|
| Description: | Computes density function, cumulative distribution function, quantile function and random numbers for a multisection composite distribution specified by the user. Also fits the user specified distribution to a given data set. More details of the package can be found in the following paper submitted to the R journal Wiegand M and Nadarajah S (2017) CompDist: Multisection composite distributions. |
| Authors: | Martin Wiegand and Saralees Nadarajah |
| Maintainer: | Saralees Nadarajah <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0 |
| Built: | 2024-10-25 06:26:14 UTC |
| Source: | CRAN |
Returns a density function of a user specified multisection composite distribution
dcomp(xx,dists,par,borders,par.pos,buffer)dcomp(xx,dists,par,borders,par.pos,buffer)
xx |
Evaluation locations |
dists |
A vector of strings stating the desired partial distributions in order |
par |
A list of parameters, a vector of parameters for each partial distribution, with the first two being the interval limits and the second argument being the weights to be used |
borders |
Optional: If the distribution has to have continuous and differentiable catentation points, the user specifies a list for each of area following the first, containing a range for a parameter of the following partial distribution to lie within. |
par.pos |
Optional: If 'borders' is non empty, e.g a smooth function is desired, here the vector of parameter positions that need to be changed is specified. Default value is 1, meaning the first parameter for each partial distribution is amended |
buffer |
Optional: A two dimensional vector, containing the values for upper and lower buffer from the respective catenation points during optimization |
An object of the same length as xx, giving the density values
Martin Wiegand, Saralees Nadarajah
par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) x<-seq(0,3,0.01) # non-continuous case y1<-dcomp(x,distvec,par) # continuous case y2<-dcomp(x,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) xrange<-range(x) yrange<-range(y1,y2) plot(x,y1,type="l",xlab="x",ylab="Density function",xlim=xrange,ylim=yrange) abline(v=1) plot(x,y2,type="l",xlab="x",ylab="Density function",xlim=xrange,ylim=yrange) abline(v=1)par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) x<-seq(0,3,0.01) # non-continuous case y1<-dcomp(x,distvec,par) # continuous case y2<-dcomp(x,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) xrange<-range(x) yrange<-range(y1,y2) plot(x,y1,type="l",xlab="x",ylab="Density function",xlim=xrange,ylim=yrange) abline(v=1) plot(x,y2,type="l",xlab="x",ylab="Density function",xlim=xrange,ylim=yrange) abline(v=1)
Returns the parameters fitted to a random sample along with a number of error measures, such as the log likelihood, AIC, BIC, AICc, CAIC and HQC.
par.fit(data,dists,par,borders,par.pos,optit,buffer,cont)par.fit(data,dists,par,borders,par.pos,optit,buffer,cont)
data |
Data set to be fitted to the distribution |
dists |
A vector of strings stating the desired partial distributions in order |
par |
A list of parameters, a vector of parameters for each partial distribution, with the first two being the interval limits and the second argument being he weights to be used |
borders |
Optional: If the distribution has to have continuous and differentiable catentation points, the user specifies a list for each of area following the first, containing a range for a parameter of the following partial distribution to lie within. |
par.pos |
Optional: If 'borders' is non empty, e.g a smooth function is desired, here the vector of parameter positions that need to be changed is specified. Default value is 1, meaning the first parameter for each partial distribution is amended |
optit |
Number of iteration loops over the parameter optimisation |
buffer |
Optional: A two dimensional vector, containing the values for upper and lower buffer from the respective catenation points during optimization |
cont |
Logical value for smooth catenation points. Default FALSE. |
Gives parameter estimates and values of the log likelihood, AIC, BIC, AICc, CAIC and HQC.
Martin Wiegand, Saralees Nadarajah
# Generate random data par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) n<-1000 # non-continuous case r1<-rcomp(n,distvec,par) # continuous case r2<-rcomp(n,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) # Initial Guess par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,0.5) par[[4]]<-c(0.5,1) # Fitting # non-continuous case estimate1<-par.fit(r1,distvec,par,optit=1) # continuous case estimate2<-par.fit(r2,distvec,par,borders=list(c(0.00001,10)),optit=1,buffer=c(10e-5,0),cont=TRUE) x<-seq(0,30,0.01) # non-continuous case y1<-dcomp(x,distvec,estimate1$Parameter) # continuous case y2<-dcomp(x,distvec,estimate2$Parameter,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) hist(r1,probability=TRUE,breaks=40,main="",xlab="Data",ylab="Fitted density") lines(x,y1,col="red") hist(r2,probability=TRUE,breaks=40,main="",xlab="Data",ylab="Fitted density") lines(x,y2,col="red") estimate1 estimate2# Generate random data par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) n<-1000 # non-continuous case r1<-rcomp(n,distvec,par) # continuous case r2<-rcomp(n,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) # Initial Guess par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,0.5) par[[4]]<-c(0.5,1) # Fitting # non-continuous case estimate1<-par.fit(r1,distvec,par,optit=1) # continuous case estimate2<-par.fit(r2,distvec,par,borders=list(c(0.00001,10)),optit=1,buffer=c(10e-5,0),cont=TRUE) x<-seq(0,30,0.01) # non-continuous case y1<-dcomp(x,distvec,estimate1$Parameter) # continuous case y2<-dcomp(x,distvec,estimate2$Parameter,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) hist(r1,probability=TRUE,breaks=40,main="",xlab="Data",ylab="Fitted density") lines(x,y1,col="red") hist(r2,probability=TRUE,breaks=40,main="",xlab="Data",ylab="Fitted density") lines(x,y2,col="red") estimate1 estimate2
Returns a cumulative distribution function of a user specified multisection composite distribution
pcomp(xx,dists,par,borders,par.pos,buffer)pcomp(xx,dists,par,borders,par.pos,buffer)
xx |
Evaluation locations |
dists |
A vector of strings stating the desired partial distributions in order |
par |
A list of parameters, a vector of parameters for each partial distribution, with the first two being the interval limits and the second argument being he weights to be used |
borders |
Optional: If the distribution has to have continuous and differentiable catentation points, the user specifies a list for each of area following the first, containing a range for a parameter of the following partial distribution to lie within. |
par.pos |
Optional: If 'borders' is non empty, e.g a smooth function is desired, here the vector of parameter positions that need to be changed is specified. Default value is 1, meaning the first parameter for each partial distribution is amended |
buffer |
Optional: A two dimensional vector, containing the values for upper and lower buffer from the respective catenation points during optimization |
An object of the same length as xx, giving the cumulative distribution function values
Martin Wiegand, Saralees Nadarajah
par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) x<-seq(0,3,0.01) # non-continuous case y1<-pcomp(x,distvec,par) # continuous case y2<-pcomp(x,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) xrange<-range(x) yrange<-range(y1,y2) plot(x,y1,type="l",xlab="x",ylab="Distribution function",xlim=xrange,ylim=yrange) abline(v=1,lty=2) plot(x,y2,type="l",xlab="x",ylab="Distribution function",xlim=xrange,ylim=yrange) abline(v=1,lty=2)par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) x<-seq(0,3,0.01) # non-continuous case y1<-pcomp(x,distvec,par) # continuous case y2<-pcomp(x,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) xrange<-range(x) yrange<-range(y1,y2) plot(x,y1,type="l",xlab="x",ylab="Distribution function",xlim=xrange,ylim=yrange) abline(v=1,lty=2) plot(x,y2,type="l",xlab="x",ylab="Distribution function",xlim=xrange,ylim=yrange) abline(v=1,lty=2)
Returns a quantile function to the specifications of a user specified multisection composite distribution
qcomp(xx,dists,par,borders,par.pos,buffer)qcomp(xx,dists,par,borders,par.pos,buffer)
xx |
Desired quantiles between 0 and 1 |
dists |
A vector of strings stating the desired partial distributions in order |
par |
A list of parameters, a vector of parameters for each partial distribution, with the first two being the interval limits and the second argument being he weights to be used |
borders |
Optional: If the distribution has to have continuous and differentiable catentation points, the user specifies a list for each of area following the first, containing a range for a parameter of the following partial distribution to lie within. |
par.pos |
Optional: If 'borders' is non empty, e.g a smooth function is desired, here the vector of parameter positions that need to be changed is specified. Default value is 1, meaning the first parameter for each partial distribution is amended |
buffer |
Optional: A two dimensional vector, containing the values for upper and lower buffer from the respective catenation points during optimization |
An object of the same length as xx, giving the quantile values
Martin Wiegand, Saralees Nadarajah
par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) x<-seq(0.01,0.99,0.01) # non-continuous case y1<-qcomp(x,distvec,par) # continuous case y2<-qcomp(x,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) xrange<-range(x) yrange<-range(y1,y2) plot(x,y1,type="l",xlab="x",ylab="Quantile function",xlim=xrange,ylim=yrange) abline(h=1,lty=2) plot(x,y2,type="l",xlab="x",ylab="Quantile function",xlim=xrange,ylim=yrange) abline(h=1,lty=2)par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) x<-seq(0.01,0.99,0.01) # non-continuous case y1<-qcomp(x,distvec,par) # continuous case y2<-qcomp(x,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) xrange<-range(x) yrange<-range(y1,y2) plot(x,y1,type="l",xlab="x",ylab="Quantile function",xlim=xrange,ylim=yrange) abline(h=1,lty=2) plot(x,y2,type="l",xlab="x",ylab="Quantile function",xlim=xrange,ylim=yrange) abline(h=1,lty=2)
Returns a random sample of size n of a user specified multisection composite distribution
rcomp(nn,dists,par,borders,par.pos,buffer)rcomp(nn,dists,par,borders,par.pos,buffer)
nn |
Desired random sample size |
dists |
A vector of strings stating the desired partial distributions in order |
par |
A list of parameters, a vector of parameters for each partial distribution, with the first two being the interval limits and the second argument being he weights to be used |
borders |
Optional: If the distribution has to have continuous and differentiable catentation points, the user specifies a list for each of area following the first, containing a range for a parameter of the following partial distribution to lie within. |
par.pos |
Optional: If 'borders' is non empty, e.g a smooth function is desired, here the vector of parameter positions that need to be changed is specified. Default value is 1, meaning the first parameter for each partial distribution is amended |
buffer |
Optional: A two dimensional vector, containing the values for upper and lower buffer from the respective catenation points during optimization |
An object of length nn, giving the random numbers
Martin Wiegand, Saralees Nadarajah
par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) n<-1000 # non-continuous case y1<-rcomp(n,distvec,par) # continuous case y2<-rcomp(n,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) hist(y1,nclass=10,xlab="x",ylab="Frequency",main="") hist(y2,nclass=10,xlab="x",ylab="Frequency",main="")par<-list() distvec<-c("lnorm","gamma") par[[1]]<-c(0,1,Inf) par[[2]]<-c(1) par[[3]]<-c(0,1) par[[4]]<-c(1,1) n<-1000 # non-continuous case y1<-rcomp(n,distvec,par) # continuous case y2<-rcomp(n,distvec,par,borders=list(c(0.00001,10)),buffer=c(10e-5,0)) par(mfrow=c(1,2),oma=rep(0,4)) hist(y1,nclass=10,xlab="x",ylab="Frequency",main="") hist(y2,nclass=10,xlab="x",ylab="Frequency",main="")