Compounding (version 1.0.2)

pgfbinomialpoisson: Function pgfbinomialpoisson

Description

This function calculates value of the pgf of the binomial-Poisson distribution.

Usage

pgfbinomialpoisson(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 binomial-Poisson distribution, such that params<-c(theta,p,n), where theta is the positive number, p is the probability, and n is the positive integer.

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(4,.5,2)
pgfbinomialpoisson(.5,params)


## The function is currently defined as
pgfbinomialpoisson <- 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]
    p<-params[2]
    n<-params[3]
if (theta<=0)
stop ("Parameter theta must be positive")
if ((p>=1)|(p<=0))
stop ("Parameter p belongs to the interval (0,1)")
if (n<0)
     stop("Parameter n must be positive")
 if(!(abs(n-round(n))<.Machine$double.eps^0.5))
stop("Parameter n must be positive integer")
   (1-p+p*exp(theta*(s-1)))^n
}