Compounding (version 1.0.2)

pgfDpoissonpascal: Function pgfDpoissonpascal.

Description

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

Usage

pgfDpoissonpascal(s, params)

Arguments

s

Value of the parameter of the pgf. It should be from interval [-1,1]. In the opposite pgf diverges.

params

List of the parameters of the Poisson-Pascal distribution, such that params<-c(theta,p,k), where all parameters are positive.

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(5,.4,.3)
pgfDpoissonpascal(.5,params)

## The function is currently defined as

pgfDpoissonpascal <- function(s,params) {
m<-s[abs(s)>1]
if (length(m)>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]
    p<-params[2]
    k<-params[3]
if (theta<=0)
    stop ("Parameter theta must be positive")
if (p<=0)
    stop ("Parameter lambda must be positive")
if (k<=0)
    stop ("Parameter k must be positive")
    theta*k*p*(1+p-p*s)^(-k-1)*exp(theta*((1+p-p*s)^(-k)-1))
}