pgfDpoissonbinomial {Compounding} R Documentation

## Function pgfDpoissonbinomial.

### Description

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

### Usage

```pgfDpoissonbinomial(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 Poisson-binomial distribution, such that params<-c(theta,p,n), where theta is the positive number, p is the probability, n is the 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

```params<-c(2.6,.7,3)
pgfDpoissonbinomial(.5,params)

## The function is currently defined as

pgfDpoissonbinomial <- 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[1]
p<-params[2]
n<-params[3]
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")
n*theta*p*(1-p+p*s)^(n-1)*exp(theta*((1-p+p*s)^n-1))
}
```

[Package Compounding version 1.0.2 Index]