Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Quantlet: INSmgfs Description: returns the moment generating function or its k-th derivative (up to third) for a light tailed distribution.

Reference(s):
P. Cizek, W. Haerdle, R. Weron (2004): "Statistical Tools for Finance and Insurance"

 Usage: y = INSmgfs(x, distrib, k, dparameters) Input: x scalar, n x 1 vector or m x n matrix, argument of the moment generating function distrib string, name of distribution, either gamma, exponential or mixofexps k scalar, integer, 0 =< k <= 3, order of the derivative dparameters list of scalars, parameters of gamma or exponential distributions list of n x 1 vectors of parameters of "mixofexps" distribution, the first vector are parameters for the exponential distributions and the second one are the weights of mixing Output: y scalar, n x 1 vector or m x n matrix (same dimension as x), moment generating function from the distribution or its k-th derivative.

Example:
```library("insurance")
library("plot")
distrib = "gamma"
dparameters = list(0.2,0.7)
x = #(0:10)/50
y = INSmgfs(x, distrib, 1, dparameters)
y
disp = createdisplay(1,1)
setgopt(disp, 1, 1,"xvalue",0|1,"yvalue",0|1)

```
Result:
```Moment generating function of gamma distribution
and its plot:

Contents of y

[ 1,]  0.28571
[ 2,]  0.29583
[ 3,]  0.30662
[ 4,]  0.31815
[ 5,]  0.33051
[ 6,]  0.34377
[ 7,]  0.35804
[ 8,]  0.37344
[ 9,]   0.3901
[10,]  0.40817
[11,]  0.42784
```

Author: P. Mista, 20031218 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006