lmomco (version 2.3.1)

ralmomco: Alpha-Percentile Residual Quantile Function of the Distributions

Description

This function computes the \(\alpha\)-Percentile Residual Quantile Function for quantile function \(x(F)\) (par2qua, qlmomco). The function is defined by Nair and Vineshkumar (2011, p. 85) and Nair et al. (2013, p. 56) as $$P_\alpha(u) = x(1 - [1-\alpha][1-u]) - x(u)\mbox{,}$$ where \(P_\alpha(u)\) is the \(\alpha\)-percentile residual quantile for nonexceedance probability \(u\) and percentile \(\alpha\) and \(x(u)\) is a constant for \(x(F = u)\). The reversed \(\alpha\)-percentile residual quantile is available under rralmomco.

Usage

ralmomco(f, para, alpha=0)

Arguments

f

Nonexceedance probability (\(0 \le F \le 1\)).

para

The parameters from lmom2par or vec2par.

alpha

The \(\alpha\) percentile, which is divided by \(100\) inside the function ahead of calling the quantile function of the distribution.

Value

\(\alpha\)-percentile residual quantile value for \(F\).

References

Nair, N.U., and Vineshkumar, B., 2011, Reversed percentile residual life and related concepts: Journal of the Korean Statistical Society, v. 40, no. 1, pp. 85--92.

Nair, N.U., Sankaran, P.G., and Balakrishnan, N., 2013, Quantile-based reliability analysis: Springer, New York.

See Also

qlmomco, rmlmomco, rralmomco

Examples

# NOT RUN {
# It is easiest to think about residual life as starting at the origin, units in days.
A <- vec2par(c(0.0, 2649, 2.11), type="gov") # so set lower bounds = 0.0
maximum.lifetime <- quagov(1,A) # 2649 days
ralmomco(0,A,alpha=0)   #    0 days
ralmomco(0,A,alpha=100) # 2649 days
ralmomco(1,A,alpha=0)   #    0 days (death certain)
ralmomco(1,A,alpha=100) #    0 days (death certain)
# }
# NOT RUN {
F <- nonexceeds(f01=TRUE)
plot(F, qlmomco(F,A), type="l",
     xlab="NONEXCEEDANCE PROBABILITY", ylab="LIFETIME, IN DAYS")
lines(F, rmlmomco(F, A), col=4, lwd=4) # thick blue, residual mean life
lines(F, ralmomco(F, A, alpha=50), col=2) # solid red, median residual life
lines(F, ralmomco(F, A, alpha=10), col=2, lty=2) # lower dashed line,
                                              # the 10th percentile of residual life
lines(F, ralmomco(F, A, alpha=90), col=2, lty=2) # upper dashed line,
                                              # 10th percentile of residual life
# }