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.
lmomcau(para)An R
list is returned.
Vector of the trimmed L-moments. First element is \(\lambda^{(1)}_1\), second element is \(\lambda^{(1)}_2\), and so on.
Vector of the L-moment ratios. Second element is \(\tau^{(1)}\), third element is \(\tau^{(1)}_3\) and so on.
Level of symmetrical trimming used in the computation, which is unity.
Level of left-tail trimming used in the computation, which is unity.
Level of right-tail trimming used in the computation, which is unity.
An attribute identifying the computational source of the L-moments: “lmomcau”.
The parameters of the distribution.
W.H. Asquith
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.
parcau, cdfcau, pdfcau, quacau
X1 <- rcauchy(20)
lmomcau(parcau(TLmoms(X1,trim=1)))
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