# rrmvarlmomco: Reversed Variance Residual Quantile Function of the... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many 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

 1 rrmvarlmomco(f, para) 

## Arguments

 f Nonexceedance probability (0 ≤ F ≤ 1). para The parameters from lmom2par or vec2par.

## Value

Reversed residual variance value for F.

W.H. Asquith

## References

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

qlmomco, rrmlmomco
  1 2 3 4 5 6 7 8 9 10 # 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)