parcau {lmomco} | R Documentation |
This function estimates the parameters of the Cauchy distribution from the trimmed L-moments (TL-moments) having trim level 1.
parcau(lmom)
lmom |
TL-moments from TLmoms with trim=1 . |
Unlike many of the other distributions in this package,
the parameter estimation occurs by passing the data into the function
and not from passing of an L-moment object (see lmom.ub
).
Contrast this practice with pargum
for example.) The reason this is so is because the usual L-moments are
undefined for the Cauchy distribution, but the trimmed L-moments with
a symmetrical trimming parameter are defined. Specifically, the L-moments by
trimming the smallest and largest order statistic expections of the Cauchy are
defined by Elamir and Seheult (2003). The function parcau
calls
TLlmoms(x,trim=1)
) internally to compute the trimmed L-moments.
The relation between the parameters and the trimmed L-moments is
xi = λ^{(1)}_1 mbox{and}
α = frac{λ^{(1)}_2}{0.698} mbox{.}
An R list
is returned.
type |
The type of distribution: cau . |
para |
The parameters of the distribution. |
source |
The source of the parameters: “parcau”. |
W.H. Asquith
Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.
Gilchrist, W.G., 2000, Statistical modeling with quantile functions: Chapman and Hall/CRC, Boca Raton, FL.
X1 <- rcauchy(20) parcau(TLmoms(X1,trim=1))