lmomco (version 2.4.14)

rrmvarlmomco: Reversed Variance Residual Quantile Function of the Distributions

Description

This function computes the Reversed Variance Residual Quantile Function for a quantile function \(x{F}\) (par2qua, qlmomco). The variance is defined by Nair et al. (2013, p. 58) as $$D(u) = \frac{1}{u} \int_0^u R(u)^2\; \mathrm{d}p\mbox{,}$$ where \(D(u)\) is the variance of \(R(u)\) (the reversed mean residual quantile function, rrmlmomco) for nonexceedance probability \(u\). The variance of \(M(u)\) is provided in rmvarlmomco.

Usage

rrmvarlmomco(f, para)

Value

Reversed residual variance 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, rrmlmomco

Examples

# It is easiest to think about residual life as starting at the origin, units in days.
A <- vec2par(c(0.0, 264, 1.6), type="gov") # so set lower bounds = 0.0
rrmvarlmomco(0.5, A) # variance at the median reversed mean residual life
if (FALSE) {
A <- vec2par(c(-100, 264, 1.6), type="gov")
F <- nonexceeds(f01=TRUE)
plot(F, rmvarlmomco(F,A), type="l")
lines(F, rrmvarlmomco(F,A), col=2)
}