# pgfbinomialpoisson: Function pgfbinomialpoisson In Compounding: Computing Continuous Distributions

## Description

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

## Usage

 `1` ```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.

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```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 } ```

Compounding documentation built on May 30, 2017, 4:02 a.m.