lmomgpaRC | R Documentation |
This function computes the “B”-type L-moments of the Generalized Pareto distribution given the parameters (\xi
, \alpha
, and \kappa
) from pargpaRC
and the right-tail censoring fraction \zeta
. The B-type L-moments in terms of the parameters are
\lambda^B_1 = \xi + \alpha m_1 \mbox{,}
\lambda^B_2 = \alpha (m_1 - m_2) \mbox{,}
\lambda^B_3 = \alpha (m_1 - 3m_2 + 2m_3)\mbox{,}
\lambda^B_4 = \alpha (m_1 - 6m_2 + 10m_3 - 5m_4)\mbox{, and}
\lambda^B_5 = \alpha (m_1 - 10m_2 + 30m_3 - 35m_4 + 14m_5)\mbox{,}
where m_r = \lbrace 1-(1-\zeta)^{r+\kappa}\rbrace/(r+\kappa)
and \zeta
is the right-tail censor fraction or the probability \mathrm{Pr}\lbrace \rbrace
that x
is less than the quantile at \zeta
nonexceedance probability: (\mathrm{Pr}\lbrace x < X(\zeta) \rbrace
). In other words, if \zeta = 1
, then there is no right-tail censoring. Finally, the RC
in the function name is to denote R
ight-tail C
ensoring.
lmomgpaRC(para)
para |
The parameters of the distribution. Note that if the |
An R list
is returned.
lambdas |
Vector of the L-moments. First element is
|
ratios |
Vector of the L-moment ratios. Second element is
|
trim |
Level of symmetrical trimming used in the computation, which is |
leftrim |
Level of left-tail trimming used in the computation, which is |
rightrim |
Level of right-tail trimming used in the computation, which is |
source |
An attribute identifying the computational source of the L-moments: “lmomgpaRC”. |
message |
For clarity, this function adds the unusual message to an L-moment object that the |
zeta |
The censoring fraction. Assumed equal to unity if not present in the |
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, v. 52, pp. 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.
pargpa
, pargpaRC
, lmomgpa
, cdfgpa
, pdfgpa
, quagpa
para <- vec2par(c(1500,160,.3),type="gpa") # build a GPA parameter set
lmorph(lmomgpa(para))
lmomgpaRC(para) # zeta = 1 is internally assumed if not available
# The previous two commands should output the same parameter values from
# independent code bases.
# Now assume that we have the sample parameters, but the zeta is nonunity.
para$zeta = .8
lmomgpaRC(para) # The B-type L-moments.
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