rrmvarlmomco {lmomco}

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.

Author(s)

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
## 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)

## End(Not run)