This function estimates the L-moments of the Gamma distribution given the parameters (\(\alpha\) and \(\beta\)) from pargam. The L-moments in terms of the parameters are complicated and solved numerically. This function is adaptive to the 2-parameter and 3-parameter Gamma versions supported by this package. For legacy reasons, lmomco continues to use a port of Hosking's FORTRAN into R if the 2-parameter distribution is used but the 3-parameter generalized Gamma distribution calls upon theoLmoms.max.ostat. Alternatively, the theoTLmoms could be used: theoTLmoms(para) is conceptually equivalent to the internal calls to theoLmoms.max.ostat made for the lmomgam implementation.
lmomgam(para, ...)An R
list is returned.
Vector of the L-moments. First element is \(\lambda_1\), second element is \(\lambda_2\), and so on.
Vector of the L-moment ratios. Second element is \(\tau\), third element is \(\tau_3\) and so on.
Level of symmetrical trimming used in the computation, which is 0.
Level of left-tail trimming used in the computation, which is NULL.
Level of right-tail trimming used in the computation, which is NULL.
An attribute identifying the computational source of the L-moments: “lmomgam”.
The parameters of the distribution.
Additional arguments to pass to theoLmoms.max.ostat.
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, p. 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.
pargam, cdfgam, pdfgam, quagam