# parst3: Estimate the Parameters of the 3-Parameter Student t... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function estimates the parameters of the 3-parameter Student t distribution given the L-moments of the data in an L-moment object such as that returned by lmoms. The relations between distribution parameters and L-moments are seen under lmomst3. The largest value of ν recognized is 1000, which is the Normal distribution and the smallest value recognized is 1.000001, which was arrived from manual experiments. As ν \rightarrow ∞ the distribution limits to the Cauchy, but the implementation here does not switch over to the Cauchy. Therefore in lmomco 1.000001 ≤ ν ≤ 1000. The ν is the “degrees of freedom” parameter that is well-known with the 1-parameter Student t distribution.

## Usage

 1 parst3(lmom, checklmom=TRUE, ...) 

## Arguments

 lmom An L-moment object created by lmoms or vec2lmom. checklmom Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the τ_4 and τ_3 inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check. ... Other arguments to pass.

## Value

An R list is returned.

 type The type of distribution: st3. para The parameters of the distribution. source The source of the parameters: “parst3”.

W.H. Asquith

## References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

lmomst3, cdfst3, pdfst3, quast3
 1 2 3 4 5  parst3(vec2lmom(c(10,2,0,.1226)))$para parst3(vec2lmom(c(10,2,0,.14)))$para parst3(vec2lmom(c(10,2,0,0.2)))$para parst3(vec2lmom(c(10,2,0,0.4)))$para parst3(vec2lmom(c(10,2,0,0.9)))\$para