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

Estimate the Parameters of the 3-Parameter Student t Distribution

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 \nu recognized is 10^5.5, which is the near the Normal distribution and the smallest value recognized is 1.001, which is near the Cauchy. As \nu \rightarrow 1 the distribution limits to the Cauchy, but the implementation here does not switch over to the Cauchy. Therefore in lmomco 1.001 \le \nu \le 10^5.5. The \nu is the “degrees of freedom” parameter that is well-known with the 1-parameter Student t distribution. The nu limits are studied in the inst/doc/t4t6/studyST3.R script and the theoTLmoms function and its performance on the quantile function of the distribution provide the guidance including range of numerically computable \tau_6. The \tau_4 value can be set as low as 0.1226 as short-hand for the true lower L-kurtosis limit, which is that of the Normal (30/\pi \times \mathrm{atan}(\sqrt{2}) - 9 = 0.1226017 and additional decimals). Internally, the given 0.1226 \le \tau_4 \le 0.1226017 is snapped to that of the Normal with an internal small positive nudge up. The \tau_4 > 0.998 are set to \tau_4 = 0.998.

Usage

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 \tau_4 and \tau_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.
rt	The returned list of the uniroot() call to estimate \nu.
source	The source of the parameters: “parst3”.

Author(s)

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.

See Also

lmomst3, cdfst3, pdfst3, quast3

Examples

  parst3(vec2lmom(c(10, 2, 0, 0.1226)))$para
  parst3(vec2lmom(c(10, 2, 0, 0.14  )))$para
  parst3(vec2lmom(c(10, 2, 0, 0.4   )))$para
  parst3(vec2lmom(c(10, 2, 0, 0.9   )))$para
  parst3(vec2lmom(c(10, 2, 0, 0.998 )))$para

lmomco documentation built on May 29, 2024, 10:06 a.m.