Alpha-Percentile Residual Quantile Function of the Distributions

Description

This function computes the α-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_α(u) = x(1 - [1-α][1-u]) - x(u)\mbox{,}

where P_α(u) is the α-percentile residual quantile for nonexceedance probability u and percentile α and x(u) is a constant for x(F = u). The reversed α-percentile residual quantile is available under rralmomco.

Usage

1
ralmomco(f, para, alpha=0)

Arguments

f

Nonexceedance probability (0 ≤ F ≤ 1).

para

The parameters from lmom2par or vec2par.

alpha

The α percentile, which is divided by 100 inside the function ahead of calling the quantile function of the distribution.

Value

α-percentile residual quantile value for F.

Author(s)

W.H. Asquith

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

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# 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
## End(Not run)

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