lmomrevgum {lmomco} | R Documentation |
This function estimates the L-moments of the Reverse Gumbel distribution given
the parameters (xi and α) from parrevgum
.
The type-B L-moments in terms of the parameters are
λ^B_1 = xi - (0.5722...) α - αlbracemathrm{Ei}(-log(1-zeta))rbracembox{,}
λ^B_2 = αlbracelog(2) + mathrm{Ei}(-2log(1-zeta)) - mathrm{Ei}(-log(1-zeta))rbracembox{,}
tau_3 = mbox{,}
tau_4 = mbox{, and}
tau_5 = 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}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”. |
W.H. Asquith
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.
parrevgum
, quarevgum
, cdfrevgum
lmr <- lmom.ub(c(123,34,4,654,37,78)) rev.para <- lmom2par(lmr,type='revgum') lmomrevgum(rev.para)