GLDEX (version 2.0.0.9.3)

fun.theo.bi.mv.gld: Calculates the theoretical mean, variance, skewness and kurtosis for mixture of two generalised lambda distributions.

Description

This is the bimodal counterpart for fun.comp.moments.ml.2 and fun.comp.moments.ml.

Usage

fun.theo.bi.mv.gld(L1, L2, L3, L4, param1, M1, M2, M3, M4, param2, p1,
normalise="N")

Value

A vector showing the theoretical mean, variance, skewness and kurtosis for mixture of two generalised lambda distributions.

Arguments

L1

Location parameter of the first generalised lambda distribution. Or all the parameters of mixture distribution in the form of c(L1,L2,L3,L4,M1,M2,M3,M4,p), you still must specify param1 and param2.

L2

Scale parameter of the first generalised lambda distribution.

L3

First shape parameter of the first generalised lambda distribution.

L4

Second shape parameter of the first generalised lambda distribution.

param1

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

M1

Location parameter of the second generalised lambda distribution

M2

Scale parameter of the second generalised lambda distribution.

M3

First shape parameter of the second generalised lambda distribution.

M4

Second shape parameter of the second generalised lambda distribution.

param2

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

p1

Proportion of the first generalisd lambda distribution.

normalise

"Y" if you want kurtosis to be calculated with reference to kurtosis = 0 under Normal distribution.

Author

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

fun.moments.bimodal, fun.simu.bimodal, fun.rawmoments

Examples

# \donttest{
# Fits the Old Faithful geyser data (first column) using the maximum 
# likelihood.
 fit1<-fun.auto.bimodal.ml(faithful[,1],init1.sel="rmfmkl",init2.sel="rmfmkl",
 init1=c(-0.25,1.5),init2=c(-0.25,1.5),leap1=3,leap2=3)

# Find the theoretical moments of the fit
 fun.theo.bi.mv.gld(fit1$par[1],fit1$par[2],fit1$par[3],fit1$par[4],"fmkl",
 fit1$par[5],fit1$par[6],fit1$par[7],fit1$par[8],"fmkl",fit1$par[9])

# Compare this with the empirical moments from the data set.
 fun.moments(faithful[,1])
# }