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lmomco (version 2.4.14)

lmomcau: Trimmed L-moments of the Cauchy Distribution

Description

This function estimates the trimmed L-moments of the Cauchy distribution given the parameters (ξ and α) from parcau. The trimmed L-moments in terms of the parameters are λ1(1)=ξ, λ2(1)=0.698α, τ3(1)=0, and τ4(1)=0.343. These TL-moments (trim=1) are symmetrical for the first L-moments defined because E[X1:n] and E[Xn:n] undefined expectations for the Cauchy.

Usage

lmomcau(para)

Value

An R

list is returned.

lambdas

Vector of the trimmed L-moments. First element is λ1(1), second element is λ2(1), and so on.

ratios

Vector of the L-moment ratios. Second element is τ(1), third element is τ3(1) 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”.

Arguments

para

The parameters of the distribution.

Author

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

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

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