GLDEX: fun.RMFMKL.hs – R documentation

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fun.RMFMKL.hs

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`	Scrambling (0,1,2,3) for the Sobol sequence for the distribution fit. See scrambling/leap argument for `runif.sobol`, `runif.halton` or `QUnif`.
`FUN`	A character string of either `"runif.sobol"` (default), `"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.

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)

GLDEX

Fitting Single and Mixture of Generalised Lambda Distributions (RS and FMKL) using Various Methods

v2.0.0.7

GPL (>= 3)

Authors

Steve Su, with contributions from: Diethelm Wuertz, Martin Maechler and Rmetrics core team members for low discrepancy algorithm, Juha Karvanen for L moments codes, Robert King for gld C codes and starship codes, Benjamin Dean for corrections and input in ks.gof code and R core team for histsu function.

Initial release

2020-02-04