lmomco (version 2.4.14)

lmomgpaRC: B-type L-moments of the Generalized Pareto Distribution with Right-Tail Censoring

Description

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 Right-tail Censoring.

Usage

lmomgpaRC(para)

Value

An R

list is returned.

lambdas

Vector of the L-moments. First element is \(\lambda_1\), second element is \(\lambda_2\), and so on.

ratios

Vector of the L-moment ratios. Second element is \(\tau\), third element is \(\tau_3\) and so on.

trim

Level of symmetrical trimming used in the computation, which is 0.

leftrim

Level of left-tail trimming used in the computation, which is NULL.

rightrim

Level of right-tail trimming used in the computation, which is NULL.

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 lambdas and ratios are B-type L-moments.

zeta

The censoring fraction. Assumed equal to unity if not present in the gpa parameter object.

Arguments

para

The parameters of the distribution. Note that if the \(\zeta\) part of the parameters (see pargpaRC) is not present then zeta=1 (no right-tail censoring) is assumed.

Author

W.H. Asquith

References

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.

See Also

pargpa, pargpaRC, lmomgpa, cdfgpa, pdfgpa, quagpa

Examples

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.