pgfyule {Compounding} R Documentation

## Function pgfyule

### Description

This function calculates value of the pgf of the Yule distribution.

### Usage

```pgfyule(s, params)
```

### Arguments

 `s` Value of the parameter of the pgf. It should be from interval [-1,1]. In the opposite pgf divegrates. `params` Postive parameter of the Yule distribution, such that params<-theta.

### 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

Hankin R.K.S, Lee A (2006) A new family of non-negative distributions. Australia and New Zealand Journal of Statistics 48(1): 67(78)

http://www.am.qub.ac.uk/users/g.gribakin/sor/Chap3.pdf

### Examples

```params<-3
pgfyule(.5,params)

## The function is currently defined as

pgfyule <- function(s,params) {
require(hypergeo)
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)>1)
stop("The length of params is 1")
theta<-params[1]
if (theta<=0)
stop ("Parameter theta must be positive")
theta/(theta+1)*Re(hypergeo(1,1,theta+2,s))
}
```

[Package Compounding version 1.0.2 Index]