# pgfInegativebinomial: Function pgfInegativebinomial In Compounding: Computing Continuous Distributions

## Description

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

## Usage

 `1` ```pgfInegativebinomial(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 negative binomial distribution, such that params<-c(theta,k), where theta is probability, and k is positive number.

## 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``` ```params<-c(.9,.7) pgfInegativebinomial(.5,params) ## The function is currently defined as pgfDnegativebinomial <- function(s,params) { k<-s[abs(s)>1] if (length(k)>0) warning("Some elements of the vector s are out of interval [-1,1]") if (length(params)<2) stop("At least one value in params is missing") if (length(params)>2) stop("The length of params is 2") theta<-params[1] k<-params[2] if ((theta>=1)|(theta<=0)) stop ("Parameter theta belongs to the interval (0,1)") if (k<=0) stop("Parameter k must be positive") k*(1-theta)*theta^k/(1-(1-theta)*s)^(k+1) } ```

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