pgfnegativebinomial {Compounding} R Documentation

## Function pgfnegativebinomial

### Description

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

### Usage

```pgfnegativebinomial(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

```params<-c(.2,.3)
pgfnegativebinomial(.5,params)

## The function is currently defined as

pgfnegativebinomial <- 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
k<-params
if ((theta>=1)|(theta<=0))
stop ("Parameter theta belongs to the interval (0,1)")
if (k<=0)
stop("Parameter k must be positive")
(theta/(1-(1-theta)*s))^k
}

```

[Package Compounding version 1.0.2 Index]