Bpwm2ApwmRC {lmomco} | R Documentation |
This function converts “B”-type Probability-Weighted Moments (PWMs, β^B_r) to the “A”-type β^A_r. The β^A_r are the ordinary PWMs for the m left noncensored or observed values. The β^B_r are more complex and use the m observed values and the m-n right-tailed censored values for which the censoring threshold is known. These PWMs are described in the documentation for pwmRC
.
This function uses the defined relation between to two PWM types when the β^B_r are known along with the parameters (para
) of a right-tail censored distribution inclusive of the censoring fraction zeta=m/n. The value 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).
β^A_{r-1} = frac{rβ^B_{r-1} - (1-zeta^r)X(zeta)}{rzeta^r} mbox{,}
where 1 <= r <= n and n is the number of moments, and X(zeta) is the value of the quantile function at nonexceedance probability zeta. Finally, the RC
in the function name is to denote R
ight-tail C
ensoring.
Bpwm2ApwmRC(Bpwm,para)
Bpwm |
A vector of B-type PWMs: β^B_r |
para |
The parameters of the distribution from a function such as pargpaRC in which the β^B_r are contained in a list element titled betas and the right-tail censoring fraction zeta is contained in an element titled zeta . |
An R list
is returned.
W.H. Asquith
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.
Apwm2BpwmRC
and pwmRC
# 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