tlmrgev: Compute Select TL-moment ratios of the Generalized Extreme... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Description

This function computes select TL-moment ratios of the Generalized Extreme Value distribution for defaults of ξ = 0 and α = 1. This function can be useful for plotting the trajectory of the distribution on TL-moment ratio diagrams of τ^{(t_1,t_2)}_2, τ^{(t_1,t_2)}_3, τ^{(t_1,t_2)}_4, τ^{(t_1,t_2)}_5, and τ^{(t_1,t_2)}_6. In reality, τ^{(t_1,t_2)}_2 is dependent on the values for ξ and α. If the message

 1 Error in integrate(XofF, 0, 1) : the integral is probably divergent

occurs then careful adjustment of the shape parameter κ parameter range is very likely required. Remember that TL-moments with nonzero trimming permit computation of TL-moments into parameter ranges beyond those recognized for the usual (untrimmed) L-moments.

Usage

 1 2 tlmrgev(trim=NULL, leftrim=NULL, rightrim=NULL, xi=0, alpha=1, kbeg=-.99, kend=10, by=.1)

Arguments

 trim Level of symmetrical trimming to use in the computations. Although NULL in the argument list, the default is 0—the usual L-moment ratios are returned. leftrim Level of trimming of the left-tail of the sample. rightrim Level of trimming of the right-tail of the sample. xi Location parameter of the distribution. alpha Scale parameter of the distribution. kbeg The beginning κ value of the distribution. kend The ending κ value of the distribution. by The increment for the seq() between kbeg and kend.

Value

An R list is returned.

 tau2 A vector of the τ^{(t_1,t_2)}_2 values. tau3 A vector of the τ^{(t_1,t_2)}_3 values. tau4 A vector of the τ^{(t_1,t_2)}_4 values. tau5 A vector of the τ^{(t_1,t_2)}_5 values. tau6 A vector of the τ^{(t_1,t_2)}_6 values.

Note

The function uses numerical integration of the quantile function of the distribution through the theoTLmoms function.

W.H. Asquith