| Type: | Package |
| Title: | Multisection Composite Distributions |
| Version: | 1.0 |
| Author: | Martin Wiegand and Saralees Nadarajah |
| Date: | 2017-08-16 |
| Maintainer: | Saralees Nadarajah <Saralees.Nadarajah@manchester.ac.uk> |
| Depends: | R (≥ 3.3.0), numDeriv |
| Imports: | fExtremes, actuar, VGAM, rmutil, PearsonDS |
| 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. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2017-08-17 11:25:55 UTC; mbbsssn2 |
| Repository: | CRAN |
| Date/Publication: | 2017-08-17 11:38:03 UTC |
dcomp
Description
Returns a density function of a user specified multisection composite distribution
Usage
dcomp(xx,dists,par,borders,par.pos,buffer)
Arguments
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 |
Value
An object of the same length as xx, giving the density values
Author(s)
Martin Wiegand, Saralees Nadarajah
Examples
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.fit
Description
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.
Usage
par.fit(data,dists,par,borders,par.pos,optit,buffer,cont)
Arguments
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. |
Value
Gives parameter estimates and values of the log likelihood, AIC, BIC, AICc, CAIC and HQC.
Author(s)
Martin Wiegand, Saralees Nadarajah
Examples
# 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
estimate2pcomp
Description
Returns a cumulative distribution function of a user specified multisection composite distribution
Usage
pcomp(xx,dists,par,borders,par.pos,buffer)
Arguments
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 |
Value
An object of the same length as xx, giving the cumulative distribution function values
Author(s)
Martin Wiegand, Saralees Nadarajah
Examples
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)qcomp
Description
Returns a quantile function to the specifications of a user specified multisection composite distribution
Usage
qcomp(xx,dists,par,borders,par.pos,buffer)
Arguments
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 |
Value
An object of the same length as xx, giving the quantile values
Author(s)
Martin Wiegand, Saralees Nadarajah
Examples
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)rcomp
Description
Returns a random sample of size n of a user specified multisection composite distribution
Usage
rcomp(nn,dists,par,borders,par.pos,buffer)
Arguments
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 |
Value
An object of length nn, giving the random numbers
Author(s)
Martin Wiegand, Saralees Nadarajah
Examples
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="")