Description Usage Arguments Value Author(s) References See Also Examples

This function converts “A”-type probability-weighted moments (PWMs, *β^A_r*) to the “B”-type *β^B_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. 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 *β^A_r* are known along with the parameters (`para`

) of a right-tail censored distribution inclusive of the censoring fraction *ζ=m/n*. The value *ζ* is the right-tail 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*). The relation is

*β^B_{r-1} = r^{-1}\lbraceζ^r r β^A_{r-1} + (1-ζ^r)X(ζ)\rbrace \mbox{,}*

where *1 ≤ r ≤ n* and *n* is the number of moments, and *X(ζ)* is the value of the quantile function at nonexceedance probability *ζ*. Finally, the `RC`

in the function name is to denote `R`

ight-tail `C`

ensoring.

1 | ```
Apwm2BpwmRC(Apwm,para)
``` |

`Apwm` |
A vector of A-type PWMs: |

`para` |
The parameters of the distribution from a function such as |

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# 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
Bbetas <- Apwm2BpwmRC(z$Abetas,para)
Abetas <- Bpwm2ApwmRC(Bbetas$betas,para)
# Assertion that both of the vectors of B-type PWMs should be the same.
str(Abetas) # A-type PWMs of the distribution
str(z$Abetas) # A-type PWMs of the original data
``` |

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