pgfDkattitypeh1 {Compounding} R Documentation

## Function pgfDkattitypeh1

### Description

This function calculates value of the pgf's first derivative of the Katti type H1 distribution.

### Usage

```pgfDkattitypeh1(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 Katti type H1 distribution, such that params<-c(theta,a,b), where all parameter 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(.4,9,5)
pgfDkattitypeh1(.5,params)

## The function is currently defined as

pgfDkattitypeh1 <- 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)<3)
stop("At least one value in params is missing")
if (length(params)>3)
stop("The length of params is 3")
theta<-params
a<-params
b<-params
if (theta<=0)
stop ("Parameter theta must be positive")
if (a<=0)
stop ("Parameter a must be positive")
if (b<=0)
stop ("Parameter b must be positive")
a*theta/(a+b)*genhypergeo(a+1,a+b+1,theta*(s-1))
}
```

[Package Compounding version 1.0.2 Index]