lmomgev {lmomco} | R Documentation |
This function estimates the L-moments of the Generalized Extreme Value distribution given the parameters
(xi, α, and kappa) from pargev
.
The L-moments in terms of the parameters are
λ_1 = xi + frac{α}{kappa}(1-Γ(1+kappa)) mbox{,}
λ_2 = frac{α}{kappa}(1-2^{-kappa})Γ(1+kappa) mbox{,}
tau_3 = frac{2(1-3^{-kappa})}{1-2^{-kappa}} - 3 mbox{, and}
tau_4 = frac{5(1-4^{-kappa})-10(1-3^{-kappa})+6(1-2^{-kappa})}{1-2^{-kappa}} mbox{.}
lmomgev(para)
para |
The parameters of the distribution. |
An R list
is returned.
L1 |
Arithmetic mean. |
L2 |
L-scale—analogous to standard deviation. |
LCV |
coefficient of L-variation—analogous to coefficient of variation. |
TAU3 |
The third L-moment ratio or L-skew—analogous to skew. |
TAU4 |
The fourth L-moment ratio or L-kurtosis—analogous to kurtosis. |
TAU5 |
The fifth L-moment ratio. |
L3 |
The third L-moment. |
L4 |
The fourth L-moment. |
L5 |
The fifth L-moment. |
source |
An attribute identifying the computational source of the L-moments: “lmomgev”. |
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, vol. 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.
lmr <- lmom.ub(c(123,34,4,654,37,78)) lmr lmomgev(pargev(lmr))