fun.rawmoments {GLDEX}

Computes the raw moments of the generalised lambda distribution up to 4th order.

Description

This function is of theoretical interest only.

Usage

fun.rawmoments(L1, L2, L3, L4, param = "fmkl")

Arguments

L1

Location parameter of the generalised lambda distribution.

L2

Scale parameter of the generalised lambda distribution.

L3

First shape parameter of the generalised lambda distribution.

L4

Second shape parameter of the generalised lambda distribution.

param

"rs" or "fmkl" specifying the type of the generalised lambda distribution.

Details

This function is the building block for fun.theo.bi.mv.gld.

Value

A vector showing the raw moments of the specified generalised lambda distribution up to the fourth order.

Author(s)

Steve Su

References

Freimer, M., Mudholkar, G. S., Kollia, G. & Lin, C. T. (1988), A study of the generalized tukey lambda family, Communications in Statistics - Theory and Methods *17*, 3547-3567.

Karian, Zaven A. and Dudewicz, Edward J. (2000), Fitting statistical distributions: the Generalized Lambda Distribution and Generalized Bootstrap methods, Chapman & Hall

Ramberg, J. S. & Schmeiser, B. W. (1974), An approximate method for generating asymmetric random variables, Communications of the ACM *17*, 78-82.

See Also

~~objects to See Also as help, ~~~

Examples

## Generate some random numbers using FMKL and RS generalised lambda 
## distributions and then compute the empirical and theoretical 
## E(X), E(X^2), E(X^3), E(X^4) 

junk<-rgl(100000,1,2,3,4)
mean(junk)
mean(junk^2)
mean(junk^3)
mean(junk^4)

junk<-rgl(100000,1,2,3,4,"rs")
mean(junk)
mean(junk^2)
mean(junk^3)
mean(junk^4)

fun.rawmoments(1,2,3,4)
fun.rawmoments(1,2,3,4,"rs")