fun.RMFMKL.hs {GLDEX}

Fit FMKL generalised distribution to data using discretised approach with weights.

Description

This function fits FMKL generalised distribution to data using discretised approach with weights. It is designed to act as a smoother device rather than as a definitive fit.

Usage

fun.RMFMKL.hs(data, default = "Y", fmkl.init = c(-0.25, 1.5), no.c.fmkl = 50, 
leap = 3,FUN="runif.sobol",no=10000)

Arguments

data

Dataset to be fitted

default

If yes, this function uses the default method fun.nclass.e to calculate number of classes required.

fmkl.init

Initial values for FMKL distribution optimization, c(-0.25,1.5) tends to work well.

no.c.fmkl

Number of classes or bins of histogram to be optimized over. This argument is ineffective if default="Y".

leap

See scrambling argument in fun.gen.qrn.

FUN

A character string of either "runif.sobol" (default), "runif.sobol.owen", "runif.halton" or "QUnif".

no

Number of initial random values to find the best initial values for optimisation.

Details

This function optimises the deviations of frequency of the bins to that of the theoretical so it has the effect of "fitting clothes" onto the data set. The user can decide the frequency of the bins they want the distribution to smooth over. The resulting fit may or may not be an adequate fit from a formal statistical point of view such as satisfying the goodness of fit for example, but it can be useful to suggest the range of different distributions exhibited by the data set. The default number of classes calculates the mean and variance after categorising the data into different bins and uses the number of classes that best matches the mean and variance of the original, ungrouped data. The weighting is designed to accentuate the peak or the dense part of the distribution and suppress the tails.

Value

A vector representing four parametefmkl of the FMKL generalised lambda distribution.

Note

In some cases, the resulting fit may not converge, there are currently no checking mechanism in place to ensure global convergence.

Author(s)

Steve Su

References

Su, S. (2005). A Discretized Approach to Flexibly Fit Generalized Lambda Distributions to Data. Journal of Modern Applied Statistical Methods (November): 408-424.

Su (2007). Fitting Single and Mixture of Generalized Lambda Distributions to Data via Discretized and Maximum Likelihood Methods: GLDEX in R. Journal of Statistical Software: *21* 9.

See Also

fun.RMFMKL.hs.nw, fun.RPRS.hs.nw, fun.RPRS.hs, fun.data.fit.hs, fun.data.fit.hs.nw

Examples

# Using the default number of classes
 fun.RMFMKL.hs(data=rnorm(1000,3,2),default="Y",fmkl.init=c(-0.25,1.5),leap=3)
# Using 20 classes
 fun.RMFMKL.hs(data=rnorm(1000,3,2),default="N",fmkl.init=c(-0.25,1.5),
 no.c.fmkl=20,leap=3)