This function estimates the L-moments of the Reverse Gumbel distribution given
the parameters ($\xi$ and $\alpha$) from parrevgum.
The type-B L-moments in terms of the parameters are$$\lambda^B_1 = \xi - (0.5722\dots) \alpha - \alpha\lbrace\mathrm{Ei}(-\log(1-\zeta))\rbrace\mbox{,}$$
$$\lambda^B_2 = \alpha\lbrace\log(2) + \mathrm{Ei}(-2\log(1-\zeta)) - \mathrm{Ei}(-\log(1-\zeta))\rbrace\mbox{,}$$
$$\tau_3 = \mbox{,}$$
$$\tau_4 = \mbox{, and}$$
$$\tau_5 = \mbox{.}$$
where $\zeta$ is the right-tail censoring fraction of the sample o the nonexceedance probability of the right-tail censoring threshold, and $\mathrm{Ei}(x)$ is the exponential integral defined as
$$\mathrm{Ei}(X) = \int_X^{\infty} x^{-1}e^{-x}\mathrm{d}x \mbox{,}$$
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)
- para
{The parameters of the distribution.}
An R list is returned.
- L1
{Arithmetic mean.}
- L2
{L-scale---analogous to standard deviation.}
- LCV
{coefficient of L-variation---analogous to coe. of variation.}
- TAU3
{The third L-moment ratio or L-skew--analogous to skew.}
- TAU4
{The fourth L-moment ratio or L-kurtosis---analogous to kurtosis.}
- TAU5
{The fifth L-moment ratio.}
- L3
{The third L-moment.}
- L4
{The fourth L-moment.}
- L5
{The fifth L-moment.}
- 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.}
Hosking, J.R.M., 1990, L-moments---Analysis and estimation of
distributions using linear combinations of order statistics: Journal
of the Royal Statistical Society, Series B, vol. 52, p. 105--124.
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.
[object Object]
parrevgum, quarevgum, cdfrevgum
distribution