lmomco (version 2.4.14)

rmvarlmomco: Variance Residual Quantile Function of the Distributions

Description

This function computes the Variance Residual Quantile Function for a quantile function \(x(F)\) (par2qua, qlmomco). The variance is defined by Nair et al. (2013, p. 55) as $$V(u) = \frac{1}{1-u} \int_u^1 M(u)^2\; \mathrm{d}p\mbox{,}$$ where \(V(u)\) is the variance of \(M(u)\) (the residual mean quantile function, rmlmomco) for nonexceedance probability \(u\).

Usage

rmvarlmomco(f, para)

Value

Residual variance value for \(F\).

Arguments

f

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

para

The parameters from lmom2par or vec2par.

Author

W.H. Asquith

References

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

See Also

qlmomco, rmlmomco

Examples

# 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
qlmomco(0.5, A)  # The median lifetime = 1261 days
rmlmomco(0.5, A) # The average remaining life given survival to the median = 861 days
rmvarlmomco(0.5, A) # and the variance of that value.
if (FALSE) {
A <- lmom2par(vec2lmom(c(2000, 450, 0.14, 0.1)), type="kap")
F <- nonexceeds(f01=TRUE)
plot(F, qlmomco(F,A), type="l", ylim=c(100,6000),
     xlab="NONEXCEEDANCE PROBABILITY", ylab="LIFETIME OR SQRT(VAR LIFE), IN DAYS")
lines(F, sqrt( rmvarlmomco(F, A)), col=4, lwd=4) # thick blue, residual mean life
lines(F, sqrt(rrmvarlmomco(F, A)), col=2, lwd=4) # thick red, reversed resid. mean life
lines(F,   rmlmomco(F,A), col=4, lty=2); lines(F, rrmlmomco(F,A), col=2, lty=2)
lines(F,  tttlmomco(F,A), col=3, lty=2); lines(F,  cmlmomco(F,A), col=3)
}