# pgfbinomialbinomial: Function pgfbinomialbinomial In Compounding: Computing Continuous Distributions

## Description

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

## Usage

 `1` ```pgfbinomialbinomial(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-binomial distribution, such that params<-c(p1,p2,m,n), where theta is the positive number, p1, p2 are the probabilities, and m, n are the positive integers.

## 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 28``` ```params<-c(.3,.2,4,5) pgfbinomialbinomial(.5,params) ## The function is currently defined as pgfbinomialbinomial <- 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)<4) stop("At least one value in params is missing") if (length(params)>4) stop("The length of params is 4") p1<-params[1] p2<-params[2] m<-params[3] n<-params[4] if ((p1>=1)|(p1<=0)) stop ("Parameter p1 belongs to the interval (0,1)") if ((p2>=1)|(p2<=0)) stop ("Parameter p2 belongs to the interval (0,1)") if (m<0) stop("Parameter m must be positive integer") 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-p1+p1*(1-p2+p2*s)^n)^m } ```

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