lmomco (version 2.0.1)

parst3: 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 L-moments in terms of the parameters are complicated and solved numerically. The largest value of $\nu$ recognized is 1000, which is the Normal distribution and the smallest value recognized is 1.000001, which was arrived from manual experiments. As $\nu \rightarrow \infty$ the distribution limits to the Cauchy, but the implementation here does not switch over to the Cauchy. Therefore in lmomco $1.000001 \le \nu \le 1000$. The $\nu$ is the degrees of freedom parameter that is well-known with the 1-parameter Student T distribution.

Usage

parst3(lmom, checklmom=TRUE)

Arguments

lmom

A L-moment object created by lmoms or pwm2lmom.

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 $\tau_3$ inequ

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.

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: CreateSpace Independent Publishing Platform, 2nd printing, ISBN 978-1463508418.

See Also

cdfst3, lmomst3, pdfst3, quast3

Examples

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