This function estimates the parameters of the Pearson Type III 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. For the implementation in lmomco, the three parameters are \(\mu\), \(\sigma\), and \(\gamma\) for the mean, standard deviation, and skew, respectively.
parpe3(lmom, checklmom=TRUE, ...)An R
list is returned.
The type of distribution: pe3.
The parameters of the distribution.
The source of the parameters: “parpe3”.
An L-moment object created by lmoms or vec2lmom.
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.
W.H. Asquith
Hosking, J.R.M., 1990, L-moments---Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105--124.
Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.
Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.
lmompe3, cdfpe3, pdfpe3, quape3
lmr <- lmoms(rnorm(20))
parpe3(lmr)
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