lmomco (version 2.4.14)

rralmomco: Reversed Alpha-Percentile Residual Quantile Function of the Distributions

Description

This function computes the Reversed \(\alpha\)-Percentile Residual Quantile Function for quantile function \(x(F)\) (par2qua, qlmomco). The function is defined by Nair and Vineshkumar (2011, p. 87) and Midhu et al. (2013, p. 13) as $$R_\alpha(u) = x(u) - x(u[1-\alpha])\mbox{,}$$ where \(R_\alpha(u)\) is the reversed \(\alpha\)-percentile residual quantile for nonexceedance probability \(u\) and percentile \(\alpha\) and \(x(u[1-\alpha])\) is a constant for \(x(F = u[1-\alpha])\). The nonreversed \(\alpha\)-percentile residual quantile is available under ralmomco.

Usage

rralmomco(f, para, alpha=0)

Value

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

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.

Author

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.

Midhu, N.N., Sankaran, P.G., and Nair, N.U., 2013, A class of distributions with linear mean residual quantile function and it's generalizations: Statistical Methodology, v. 15, pp. 1--24.

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

See Also

qlmomco, ralmomco

Examples

# It is easiest to think about residual life as starting at the origin, units in days.
A <- vec2par(c(145, 2649, 2.11), type="gov") # so set lower bounds = 0.0
rralmomco(0.78, A, alpha=50)
if (FALSE) {
F <- nonexceeds(f01=TRUE); r <- range(rralmomco(F,A, alpha=50), ralmomco(F,A, alpha=50))
plot(F, rralmomco(F,A, alpha=50), type="l", xlab="NONEXCEEDANCE PROBABILITY",
                  ylim=r, ylab="MEDIAN RESIDUAL OR REVERSED LIFETIME, IN DAYS")
lines(F, ralmomco(F, A, alpha=50), col=2) # notice the lack of symmetry
}