pgfDpascalpoisson {Compounding} R Documentation

## Function pgfDpascalpoisson

### Description

This function calculates value of the pgf's first derivative of the Pascal Poisson distribution.

### Usage

pgfDpascalpoisson(s, params)

### Arguments

 s Value of the parameter of the pgf. It should be form interval [-1,1]. In the opposite pgf diverges. params List of the parameters of the Pascal Poisson distribution, such that params<-c(theta,mu, a), where all parameters are positive.

### Author(s)

S. Nadarajah, B. V. Popovic, M. M. Ristic

### References

Johnson N, Kotz S, Kemp A (1992) Univariate Discrete Distributions, John Wiley and Sons, New York

http://www.am.qub.ac.uk/users/g.gribakin/sor/Chap3.pdf

### Examples

params<-c(3,2,.5)
pgfDpascalpoisson(.5,params)

## The function is currently defined as

pgfDpascalpoisson <- function(s,params) {
k<-s[abs(s)>1]
if (length(k)>0)
warning("At least one element of the vector s are out of interval [-1,1]")
if (length(params)<3)
stop("At least one value in params is missing")
if (length(params)>3)
stop("The length of params is 3")
theta<-params[1]
mu<-params[2]
a<-params[3]
if (theta<=0)
stop ("Parameter theta must be positive")
if (mu<=0)
stop ("Parameter mu must be positive")
if (a<=0)
stop ("Parameter a must be positive")
mu*exp(theta*(s-1))*(1+mu/(a*theta)-mu/(a*theta)*exp(theta*(s-1)))^(-a-1)
}

[Package Compounding version 1.0.2 Index]