pgfDpolyaaeppli {Compounding} R Documentation

## Function pgfDpolyaaeppli

### Description

This function calculates value of the pgf's first derivative of the Polya Aeppli distribution.

### Usage

```pgfDpolyaaeppli(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 Polya Aeppli distribution, such that params<-c(theta,p), where theta is the positive number, and p is the probability.

### 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(5,.4)
pgfDpolyaaeppli(.5,params)

## The function is currently defined as

pgfDpolyaaeppli <- 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)<2)
stop("At least one value in params is missing")
if (length(params)>2)
stop("The length of params is 2")
theta<-params[1]
p<-params[2]
if (theta<=0)
stop ("Parameter theta must be positive")
if ((p>=1)|(p<=0))
stop ("Parameter p belongs to the interval (0,1)")
theta*(1-p)/(1-p*s)^2*exp(theta/p*((1-p)/(1-p*s)-1))
}
```

[Package Compounding version 1.0.2 Index]