lmomTLgpa {lmomco} | R Documentation |
This function estimates the symmetrical trimmed L-moments (TL-moments) for t=1 of the Generalized Pareto distribution
given the parameters (xi, α, and kappa) from parTLgpa
.
The TL-moments in terms of the parameters are
λ^{(1)}_1 = xi + frac{α(kappa+5)}{(kappa+3)(kappa+2)} mbox{,}
λ^{(1)}_2 = frac{6α}{(kappa+4)(kappa+3)(kappa+2)} mbox{,}
tau^{(1)}_3 = frac{10(1-kappa)}{9(kappa+5)} mbox{, and}
tau^{(1)}_4 = frac{5(kappa-1)(kappa-2)}{4(kappa+6)(kappa+5)} mbox{.}
lmomTLgpa(para)
para |
The parameters of the distribution. |
An R list
is returned.
lambdas |
Vector of the TL-moments. First element is λ^{(1)}_1, second element is λ^{(1)}_2, and so on. |
ratios |
Vector of the L-moment ratios. Second element is tau^{(1)}, third element is tau^{(1)}_3 and so on. |
trim |
Trim level = 1 |
source |
An attribute identifying the computational source of the TL-moments: “lmomTLgpa”. |
W.H. Asquith
Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.
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. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.
TL <- TLmoms(c(123,34,4,654,37,78,21,3400),trim=1) TL lmomTLgpa(parTLgpa(TL))