pgfDwaring {Compounding} R Documentation

## Function pgfDwaring

### Description

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

### Usage

```pgfDwaring(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 Waring distribution, such that params<-c(c,a), where \$c>a\$ and both parameters are positive.

### 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<-c(.8,.4)
pgfDwaring(.5,params)

## The function is currently defined as

pgfDwaring <- 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)<2)
stop("At least one value in params is missing")
if (length(params)>2)
stop("The length of params is 2")
cc<-params[1]
a<-params[2]
if (cc<=0)
stop ("Parameter c must be positive")
if (a<=0)
stop ("Parameter a must be positive")

a*(cc-a)/(cc*(cc+1))*Re(hypergeo(2,a+1,cc+2,s))
}
```

[Package Compounding version 1.0.2 Index]