lmomcau | R Documentation |
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)
para |
The parameters of the distribution. |
An R list
is returned.
lambdas |
Vector of the trimmed L-moments. First element is
|
ratios |
Vector of the L-moment ratios. Second element is
|
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”. |
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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