lmomco (version 2.4.14)

qualmrq: Quantile Function of the Linear Mean Residual Quantile Function Distribution

Description

This function computes the quantiles of the Linear Mean Residual Quantile Function distribution given parameters (\(\mu\) and \(\alpha\)) computed by parlmrq. The quantile function is $$x(F) = -(\alpha + \mu)\times\log(1-F) - 2\alpha\times F\mbox{,}$$ where \(x(F)\) is the quantile for nonexceedance probability \(F\), \(\mu\) is a location parameter, and \(\alpha\) is a scale parameter. The parameters must satisfy \(\mu > 0\) and \(-\mu \le \alpha < \mu\).

Usage

qualmrq(f, para, paracheck=TRUE)

Value

Quantile value for nonexceedance probability \(F\).

Arguments

f

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

para

The parameters from parlmrq or vec2par.

paracheck

A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Author

W.H. Asquith

References

Midhu, N.N., Sankaran, P.G., and Nair, N.U., 2013, A class of distributions with linear mean residual quantile function and it's generalizations: Statistical Methodology, v. 15, pp. 1--24.

See Also

cdflmrq, pdflmrq, lmomlmrq, parlmrq

Examples

lmr <- lmoms(c(3, 0.05, 1.6, 1.37, 0.57, 0.36, 2.2));
par <- parlmrq(lmr)
qualmrq(0.75,par)  
if (FALSE) {
# The distribution is said to have a linear mean residual quantile function.
# Let us have a look.
F <- nonexceeds(); par <- vec2par(c(101,21), type="lmrq")
plot(F, qlmomco(F,par), type="l", lwd=3, xlab="NONEXCEEDANCE PROBABILITY",
     ylab="LIFE TIME, RESIDUAL LIFE, OR REVERSED RESIDUAL LIFE")
lines(F, rmlmomco(F,par),  col=2, lwd=4) # heavy red line (residual life)
lines(F, rrmlmomco(F,par), col=2, lty=2) # dashed red (reversed res. life)
lines(F, cmlmomco(F,par),  col=4)        # conditional mean (blue)
# Notice that the rmlmomco() is a straight line as the name of the parent
# distribution: Linear Mean Residual Quantile Distribution suggests.
# Curiously, the reversed mean residual is not linear.
}