# fit: Fit the skew logistic distribution using L-Moments In sld: Estimation and Use of the Quantile-Based Skew Logistic Distribution

## 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 (tau3 ) `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, [email protected], 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

`sld`

## Examples

 ```1 2 3 4 5 6 7 8``` ```generated.data <- rsl(300,c(0,1,.4)) estimate1 <- fit.sld.lmom(generated.data) estimate2 <- fit.sld.lmom.given(c(0,1,.3),n=300) data(PCB1) hist(PCB1,prob=TRUE,main="PCB in Pelican Egg Yolk with SLD fit") fit.pcb <- fit.sld.lmom(PCB1) print(fit.pcb) plotsld(fit.pcb[,1],add=TRUE,col="blue") ```

### Example output

```Loading required package: lmom
Estimate  Std. Error
alpha 185.0633242 16.16993567
beta   79.5855769  8.66949465
delta   0.6566658  0.09819437
0%      25%      50%      75%     100%
-Inf 162.2182 202.3481 249.6519      Inf
```

sld documentation built on May 2, 2019, 5:53 a.m.