lmomco (version 2.3.1)

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)

Arguments

f

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

para

The parameters from lmom2par or vec2par.

Value

Reversed residual variance value for \(F\).

References

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

See Also

qlmomco, rrmlmomco

Examples

# NOT RUN {
# 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
# }
# NOT RUN {
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)
# }