fun.moments.bimodal {GLDEX}

Finds the moments of fitted mixture of generalised lambda distribution by simulation.

Description

This functions compute the mean, variance, skewness and kurtosis of the fitted generalised lambda distribution mixtures using Monte Carlo simulation.

Usage

fun.moments.bimodal(result1, result2, prop1, prop2, len = 1000, 
no.test = 1000, param1, param2)

Arguments

result1

A vector comprising four values for the first generalised lambda distribution.

result2

A vector comprising four values for the second generalised lambda distribution.

prop1

Proportion of the first generalised lambda distribution

prop2

1-prop1, this can be left unspecified.

len

Length of object for each simulation run.

no.test

Number of simulation run.

param1

This can be "rs" or "fmkl", specifying the type of the first generalised lambda distribution.

param2

This can be "rs" or "fmkl", specifying the type of the second generalised lambda distribution.

Details

There is also a theoretical computation of the moments in fun.theo.bi.mv.gld, it should be noted that the theoretical moments may not exist. The length of object in len means how many observations should be generated in each simulation run, with the number of simulation runs governed by no.test.

Value

A matrix with four columns showing the mean, variance, skewness and kurtosis of the fitted generalised lambda distribution mixtures using Monte Carlo simulation. Each row represents a simulation run.

Author(s)

Steve Su

See Also

fun.theo.bi.mv.gld, fun.simu.bimodal, fun.rawmoments

Examples

# Fitting the first column of the Old Faithful Geyser data
 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)

# After fitting compute the monte carlo moments using fun.moments.bimodal
 fun.moments.bimodal(fit1$par[1:4],fit1$par[5:8],prop1=fit1$par[9],
 param1="fmkl",param2="fmkl")

# It is also possible to compare this with the moments of the original dataset:
 fun.moments(faithful[,1])