lmomrevgum: L-moments of the Reverse Gumbel Distribution

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

L-moments of the Reverse Gumbel Distribution

Description

This function estimates the L-moments of the Reverse Gumbel distribution given the parameters (\xi and \alpha) from parrevgum. The first two type-B L-moments in terms of the parameters are

\lambda^B_1 = \xi - (0.5722\dots) \alpha - \alpha\lbrace\mathrm{Ei}(-\log(1-\zeta))\rbrace\mbox{and}

\lambda^B_2 = \alpha\lbrace\log(2) + \mathrm{Ei}(-2\log(1-\zeta)) - \mathrm{Ei}(-\log(1-\zeta))\rbrace\mbox{,}

where \zeta is the right-tail censoring fraction of the sample or the nonexceedance probability of the right-tail censoring threshold, and \mathrm{Ei}(x) is the exponential integral defined as

\mathrm{Ei}(X) = \int_X^{\infty} x^{-1}\mathrm{exp}(-x)\mathrm{d}x \mbox{,}

where \mathrm{Ei}(-\log(1-\zeta)) \rightarrow 0 as \zeta \rightarrow 1 and \mathrm{Ei}(-\log(1-\zeta)) can not be evaluated as \zeta \rightarrow 0.

Usage

lmomrevgum(para)

Arguments

para	The parameters of the distribution.

Value

An R list is returned.

lambdas	Vector of the L-moments. First element is \lambda_1, second element is \lambda_2, and so on.
ratios	Vector of the L-moment ratios. Second element is \tau, third element is \tau_3 and so on.
trim	Level of symmetrical trimming used in the computation, which is 0.
leftrim	Level of left-tail trimming used in the computation, which is NULL.
rightrim	Level of right-tail trimming used in the computation, which is NULL.
zeta	Number of samples observed (noncensored) divided by the total number of samples.
source	An attribute identifying the computational source of the L-moments: “lmomrevgum”.

Author(s)

W.H. Asquith

References

Hosking, J.R.M., 1995, The use of L-moments in the analysis of censored data, in Recent Advances in Life-Testing and Reliability, edited by N. Balakrishnan, chapter 29, CRC Press, Boca Raton, Fla., pp. 546–560.

See Also

parrevgum, cdfrevgum, pdfrevgum, quarevgum

Examples

lmr <- lmoms(c(123,34,4,654,37,78))
rev.para <- lmom2par(lmr,type='revgum')
lmomrevgum(rev.para)

lmomco documentation built on Aug. 30, 2023, 5:10 p.m.