pgfDnegativebinomial {Compounding} R Documentation

## Function pgfDnegativebinomial

### Description

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

### Usage

```pgfDnegativebinomial(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 the probability, k is the 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(.3,.2)
pgfDnegativebinomial(.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)
}
```

[Package Compounding version 1.0.2 Index]