lmomcau: 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

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”.

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.

Examples

Run this code

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

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