# Fit the skew logistic distribution using L-Moments

### Description

Fits the quantile-based Skew Logistic Distribution using L-Moments.
`fit.sld.lmom`

calculates the sample L Moments of a dataset and uses the
method of L Moments to estimate the parameters of the skew logistic distribution.
`fit.sld.lmom.given`

fits the skew logistic using user-supplied values
of the first three L Moments.

### Usage

1 2 | ```
fit.sld.lmom.given(lmoms,n=NULL)
fit.sld.lmom(data)
``` |

### Arguments

`lmoms` |
A vector of length 3, containing the first and second (sample)
L Moments and the 3rd (sample) L Moment ratio ( |

`n` |
The sample size |

`data` |
A vector containing a dataset |

### Details

The method of L-Moments estimates of the parameters of the quantile-based skew logistic distribution are:

*alpha = L1 - 6L3*

*beta = 2 L2*

*delta = 0.5*(1+3*tau3)*

Note that *L3* in the *alpha* estimate is the 3rd L-Moment, not the 3rd L-Moment
ratio (*tau3 = L3/L2*).

`fit.sld.lmom`

uses the `samlmu`

function (from
the `lmom`

package) to calculate the sample L moments, then
`fit.sld.lmom.given`

to calculate the estimates.

### Value

If the sample size is unknown (via using `fit.sld.lmom.given`

and not specifying the sample size), a vector of length 3, with the estimated parameters,
*alpha*, *beta* and *delta*.

If the sample size is known, a 3 by 2 matrix. The first column
contains the estimated parameters,
*alpha*, *beta* and *delta*,
and the second column provides asymptotic standard errors for these.

Note that if *abs(tau3) > 1/3*,
*delta hat* is beyond its allowed value of [0,1]
and the function returns an error.
Values of *abs(tau3)*, beyond
*1/3* correspond to distributions with
greater skew than the exponential / reflected exponential,
which form the limiting cases of the skew logistic distribution.

### Author(s)

Robert King, robert.king@newcastle.edu.au, http://tolstoy.newcastle.edu.au/~rking/ and Paul van Staden

### References

van Staden, P.J. and King, Robert A.R. (2015) *The quantile-based skew logistic distribution*, Statistics and Probability Letters **96** 109–116.
http://dx.doi.org/10.1016/j.spl.2014.09.001

van Staden, Paul J. 2013 *Modeling of generalized families of probability distribution in the quantile statistical universe*.
PhD thesis, University of Pretoria.
http://hdl.handle.net/2263/40265

http://tolstoy.newcastle.edu.au/rking/SLD/SLD.html

### See Also

`sld`

### Examples

1 2 3 4 5 6 7 8 |