# fun.data.fit.ml: Fit data using RS, FMKL maximum likelihood estimation and the... In GLDEX: Fitting Single and Mixture of Generalised Lambda Distributions (RS and FMKL) using Various Methods

## Description

This function fits generalised lambda distributions to data using RPRS, RMFMKL and starship methods.

## Usage

 ```1 2``` ```fun.data.fit.ml(data, rs.leap = 3, fmkl.leap = 3, rs.init = c(-1.5, 1.5), fmkl.init = c(-0.25, 1.5),FUN="runif.sobol",no=10000) ```

## Arguments

 `data` Dataset to be fitted. `rs.leap` Scrambling (0,1,2,3) for the sobol sequence for the RPRS distribution fit. See scrambling/leap argument for `runif.sobol`, `runif.halton` or `QUnif`. `fmkl.leap` Scrambling (0,1,2,3) for the sobol sequence for the RMFMKL distribution fit. See scrambling/leap argument for `runif.sobol`, `runif.halton` or `QUnif`. `rs.init` Inititial values (lambda3 and lambda4) for the RS generalised lambda distribution. `fmkl.init` Inititial values (lambda3 and lambda4) for the FMKL generalised lambda distribution. `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 consolidates `fun.RPRS.ml`, `fun.RMFMKL.ml` and `starship` and gives all the fits in one output.

## Value

A matrix showing the parameters of generalised lambda distribution for RPRS, FMFKL and STAR methods.

## Note

RPRS can sometimes fail if it is not possible to calculate the percentiles of the data set. This usually happens when the number of data point is small.

Steve Su

## References

King, R.A.R. & MacGillivray, H. L. (1999), A starship method for fitting the generalised lambda distributions, Australian and New Zealand Journal of Statistics, 41, 353-374

Su, S. (2007). Numerical Maximum Log Likelihood Estimation for Generalized Lambda Distributions. Computational statistics and data analysis 51(8) 3983-3998.

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.

`fun.RPRS.ml`, `fun.RMFMKL.ml`, `starship`, `fun.data.fit.hs`, `fun.data.fit.hs.nw` , `fun.data.fit.qs` , `fun.data.fit.mm` , `fun.data.fit.lm`
 ```1 2 3``` ```## Fitting normal(3,2) distriution using the default setting # junk<-rnorm(50,3,2) # fun.data.fit.ml(junk) ```