Description Usage Arguments Value Author(s) References See Also Examples
This function computes the “B”type Lmoments of the Generalized Pareto distribution given the parameters (ξ, α, and κ) from pargpaRC
and the righttail censoring fraction ζ. The Btype Lmoments in terms of the parameters are
λ^B_1 = ξ + α m_1 \mbox{,}
λ^B_2 = α (m_1  m_2) \mbox{,}
λ^B_3 = α (m_1  3m_2 + 2m_3)\mbox{,}
λ^B_4 = α (m_1  6m_2 + 10m_3  5m_4)\mbox{, and}
λ^B_5 = α (m_1  10m_2 + 30m_3  35m_4 + 14m_5)\mbox{,}
where m_r = \lbrace 1(1ζ)^{r+κ}\rbrace/(r+κ) and ζ is the righttail censor fraction or the probability \mathrm{Pr}\lbrace \rbrace that x is less than the quantile at ζ nonexceedance probability: (\mathrm{Pr}\lbrace x < X(ζ) \rbrace). In other words, if ζ = 1, then there is no righttail censoring. Finally, the RC
in the function name is to denote R
ighttail C
ensoring.
1  lmomgpaRC(para)

para 
The parameters of the distribution. Note that if the ζ part of the parameters (see 
An R list
is returned.
lambdas 
Vector of the Lmoments. First element is λ_1, second element is λ_2, and so on. 
ratios 
Vector of the Lmoment ratios. Second element is τ, third element is τ_3 and so on. 
trim 
Level of symmetrical trimming used in the computation, which is 
leftrim 
Level of lefttail trimming used in the computation, which is 
rightrim 
Level of righttail trimming used in the computation, which is 
source 
An attribute identifying the computational source of the Lmoments: “lmomgpaRC”. 
message 
For clarity, this function adds the unusual message to an Lmoment object that the 
zeta 
The censoring fraction. Assumed equal to unity if not present in the 
W.H. Asquith
Hosking, J.R.M., 1990, Lmoments—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 Lmoments in the analysis of censored data, in Recent Advances in LifeTesting and Reliability, edited by N. Balakrishnan, chapter 29, CRC Press, Boca Raton, Fla., pp. 546–560.
pargpa
, pargpaRC
, lmomgpa
, cdfgpa
, pdfgpa
, quagpa
1 2 3 4 5 6 7 8  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 Btype Lmoments.

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