# ralmomco: Alpha-Percentile 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 α-Percentile Residual Quantile Function for quantile function x(F) (`par2qua`, `qlmomco`). The function is defined by Nair and Vineshkumar (2011, p. 85) and Nair et al. (2013, p. 56) as

P_α(u) = x(1 - [1-α][1-u]) - x(u)\mbox{,}

where P_α(u) is the α-percentile residual quantile for nonexceedance probability u and percentile α and x(u) is a constant for x(F = u). The reversed α-percentile residual quantile is available under `rralmomco`.

## Usage

 `1` ```ralmomco(f, para, alpha=0) ```

## Arguments

 `f` Nonexceedance probability (0 ≤ F ≤ 1). `para` The parameters from `lmom2par` or `vec2par`. `alpha` The α percentile, which is divided by 100 inside the function ahead of calling the quantile function of the distribution.

## Value

α-percentile residual quantile value for F.

W.H. Asquith

## References

Nair, N.U., and Vineshkumar, B., 2011, Reversed percentile residual life and related concepts: Journal of the Korean Statistical Society, v. 40, no. 1, pp. 85–92.

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

`qlmomco`, `rmlmomco`, `rralmomco`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```# It is easiest to think about residual life as starting at the origin, units in days. A <- vec2par(c(0.0, 2649, 2.11), type="gov") # so set lower bounds = 0.0 maximum.lifetime <- quagov(1,A) # 2649 days ralmomco(0,A,alpha=0) # 0 days ralmomco(0,A,alpha=100) # 2649 days ralmomco(1,A,alpha=0) # 0 days (death certain) ralmomco(1,A,alpha=100) # 0 days (death certain) ## Not run: F <- nonexceeds(f01=TRUE) plot(F, qlmomco(F,A), type="l", xlab="NONEXCEEDANCE PROBABILITY", ylab="LIFETIME, IN DAYS") lines(F, rmlmomco(F, A), col=4, lwd=4) # thick blue, residual mean life lines(F, ralmomco(F, A, alpha=50), col=2) # solid red, median residual life lines(F, ralmomco(F, A, alpha=10), col=2, lty=2) # lower dashed line, # the 10th percentile of residual life lines(F, ralmomco(F, A, alpha=90), col=2, lty=2) # upper dashed line, # 10th percentile of residual life ## End(Not run) ```