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 \(\zeta \rightarrow 0\).
lmomrevgum(para)An R
list is returned.
Vector of the L-moments. First element is \(\lambda_1\), second element is \(\lambda_2\), and so on.
Vector of the L-moment ratios. Second element is \(\tau\), third element is \(\tau_3\) and so on.
Level of symmetrical trimming used in the computation, which is 0.
Level of left-tail trimming used in the computation, which is NULL.
Level of right-tail trimming used in the computation, which is NULL.
Number of samples observed (noncensored) divided by the total number of samples.
An attribute identifying the computational source of the L-moments: “lmomrevgum”.
The parameters of the distribution.
W.H. Asquith
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.
parrevgum, cdfrevgum, pdfrevgum, quarevgum
lmr <- lmoms(c(123,34,4,654,37,78))
rev.para <- lmom2par(lmr,type='revgum')
lmomrevgum(rev.para)
Run the code above in your browser using DataLab