Bpwm2ApwmRC {lmomco}R Documentation

Conversion between B- and A-Type Probability-Weighted Moments for Right-Tail Censoring of an Appropriate Distribution

Description

This function converts “B”-type probability-weighted moments (PWMs, βrB\beta^B_r) to the “A”-type βrA\beta^A_r. The βrA\beta^A_r are the ordinary PWMs for the mm left noncensored or observed values. The βrB\beta^B_r are more complex and use the mm observed values and the mnm-n right-tailed censored values for which the censoring threshold is known. The “A”- and “B”-type PWMs are described in the documentation for pwmRC.

This function uses the defined relation between to two PWM types when the βrB\beta^B_r are known along with the parameters (para) of a right-tail censored distribution inclusive of the censoring fraction ζ=m/n\zeta=m/n. The value ζ\zeta is the right-tail censor fraction or the probability Pr{}\mathrm{Pr}\lbrace \rbrace that xx is less than the quantile at ζ\zeta nonexceedance probability (Pr{x<X(ζ)}\mathrm{Pr}\lbrace x < X(\zeta) \rbrace). The relation is

βr1A=rβr1B(1ζr)X(ζ)rζr\mbox,\beta^A_{r-1} = \frac{r\beta^B_{r-1} - (1-\zeta^r)X(\zeta)}{r\zeta^r} \mbox{,}

where 1rn1 \le r \le n and nn is the number of moments, and X(ζ)X(\zeta) is the value of the quantile function at nonexceedance probability ζ\zeta. Finally, the RC in the function name is to denote Right-tail Censoring.

Usage

Bpwm2ApwmRC(Bpwm,para)

Arguments

Bpwm

A vector of B-type PWMs: βrB\beta^B_r.

para

The parameters of the distribution from a function such as pargpaRC in which the βrB\beta^B_r are contained in a list element titled betas and the right-tail censoring fraction ζ\zeta is contained in an element titled zeta.

Value

An R list is returned.

Author(s)

W.H. Asquith

References

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

Apwm2BpwmRC and pwmRC

Examples

# Data listed in Hosking (1995, table 29.2, p. 551)
H <- c(3,4,5,6,6,7,8,8,9,9,9,10,10,11,11,11,13,13,13,13,13,
             17,19,19,25,29,33,42,42,51.9999,52,52,52)
      # 51.9999 was really 52, a real (noncensored) data point.
z <-  pwmRC(H,52)
# The B-type PMWs are used for the parameter estimation of the
# Reverse Gumbel distribution. The parameter estimator requires
# conversion of the PWMs to L-moments by pwm2lmom().
para <- parrevgum(pwm2lmom(z$Bbetas),z$zeta) # parameter object
Abetas <- Bpwm2ApwmRC(z$Bbetas,para)
Bbetas <- Apwm2BpwmRC(Abetas$betas,para)
# Assertion that both of the vectors of B-type PWMs should be the same.
str(Bbetas)   # B-type PWMs of the distribution
str(z$Bbetas) # B-type PWMs of the original data

[Package lmomco version 2.5.1 Index]