lmomco (version 2.4.14)

pdflmrq: Probability Density Function of the Linear Mean Residual Quantile Function Distribution

Description

This function computes the probability density function of the Linear Mean Residual Quantile Function distribution given parameters computed by parlmrq. The probability density function is $$f(x) = \frac{1 - F(x)}{2\alpha\,F(x) + (\mu - \alpha)}\mbox{,}$$ where \(f(x)\) is the nonexceedance probability for quantile \(x\), \(F(x)\) is the cumulative distribution function or nonexceedance probability at \(x\), \(\mu\) is a location parameter, and \(\alpha\) is a scale parameter.

Usage

pdflmrq(x, para)

Value

Probability density (\(f\)) for \(x\).

Arguments

x

A real value vector.

para

The parameters from parlmrq or vec2par.

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, qualmrq, lmomlmrq, parlmrq

Examples

lmr <- lmoms(c(3, 0.05, 1.6, 1.37, 0.57, 0.36, 2.2))
pdflmrq(3,parlmrq(lmr))
if (FALSE) {
para.lmrq <- list(para=c(2.1043, 0.4679), type="lmrq")
para.wei  <- vec2par(c(0,2,0.9), type="wei") # note switch from Midhu et al. ordering.
F <- seq(0.01,0.99,by=.01); x <- qualmrq(F, para.lmrq)
plot(x, pdflmrq(x, para.lmrq), type="l", ylab="", lwd=2, lty=2, col=2,
     xlab="The p.d.f. of Weibull and p.d.f. of LMRQD", xaxs="i", yaxs="i",
     xlim=c(0,9), ylim=c(0,0.8))
lines(x, pdfwei(x, para.wei))
mtext("Midhu et al. (2013, Statis. Meth.)")
}