# pgfIbinomialpoisson: Function pgfIbinomialpoisson In Compounding: Computing Continuous Distributions

## Description

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

## Usage

 `1` ```pgfIbinomialpoisson(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 positive number, p is probability, and n is 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 25 26 27``` ```params<-c(.4,.9,5) pgfIbinomialpoisson(.5,params) ## The function is currently defined as pgfIbinomialpoisson <- 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 p<-params n<-params 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") zval<-(s^(1/n)-1+p)/p 1+log(zval)/theta } ```

Compounding documentation built on May 2, 2019, 1:04 p.m.