qualmrq {lmomco} | R Documentation |
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)
Arguments
f |
Nonexceedance probability ( |
para |
|
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. |
Value
Quantile value for nonexceedance probability F
.
Author(s)
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)
## Not run:
# 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.
## End(Not run)