lmomco (version 2.4.14)

rrmlmomco: Reversed Mean Residual Quantile Function of the Distributions

Description

This function computes the Reversed Mean Residual Quantile Function for quantile function \(x(F)\) (par2qua, qlmomco). The function is defined by Nair et al. (2013, p.57) as $$R(u) = x(u) - \frac{1}{u}\int_0^u x(p)\; \mathrm{d}p\mbox{,}$$ where \(R(u)\) is the reversed mean residual for nonexceedance probability \(u\) and \(x(u)\) is a constant for \(x(F = u)\).

Usage

rrmlmomco(f, para)

Value

Reversed mean residual value for \(F\).

Arguments

f

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

para

The parameters from lmom2par or vec2par.

Author

W.H. Asquith

References

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

See Also

qlmomco, rrmvarlmomco

Examples

# It is easiest to think about residual life as starting at the origin, units in days.
A <- vec2par(c(0.0, 2649, 2.6), type="gov") # so set lower bounds = 0.0
qlmomco(0.5, A)  # The median lifetime = 1005 days
rrmlmomco(0.5, A) # The reversed mean remaining life given median survival = 691 days

if (FALSE) {
F <- nonexceeds(f01=TRUE)
plot(F, qlmomco(F,A), type="l", # life
     xlab="NONEXCEEDANCE PROBABILITY", ylab="LIFETIME, IN DAYS")
lines(F,  rmlmomco(F, A), col=4, lwd=4) # thick blue, mean residual life
lines(F, rrmlmomco(F, A), col=2, lwd=4) # thick red, reversed mean residual life
}