lmomcau: Trimmed L-moments of the Cauchy Distribution

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Trimmed L-moments of the Cauchy Distribution

Description

This function estimates the trimmed L-moments of the Cauchy distribution given the parameters (\xi and \alpha) from parcau. The trimmed L-moments in terms of the parameters are \lambda^{(1)}_1 = \xi, \lambda^{(1)}_2 = 0.698\alpha, \tau^{(1)}_3 = 0, and \tau^{(1)}_4 = 0.343. These TL-moments (trim=1) are symmetrical for the first L-moments defined because \mathrm{E}[X_{1:n}] and \mathrm{E}[X_{n:n}] undefined expectations for the Cauchy.

Usage

lmomcau(para)

Arguments

para	The parameters of the distribution.

Value

An R list is returned.

lambdas	Vector of the trimmed L-moments. First element is \lambda^{(1)}_1, second element is \lambda^{(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	Level of symmetrical trimming used in the computation, which is unity.
leftrim	Level of left-tail trimming used in the computation, which is unity.
rightrim	Level of right-tail trimming used in the computation, which is unity.
source	An attribute identifying the computational source of the L-moments: “lmomcau”.

Author(s)

W.H. Asquith

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, v. 43, pp. 299–314.

See Also

parcau, cdfcau, pdfcau, quacau

Examples

X1 <- rcauchy(20)
lmomcau(parcau(TLmoms(X1,trim=1)))

lmomco documentation built on Aug. 30, 2023, 5:10 p.m.