rmvarlmomco: Variance Residual Quantile Function of the Distributions

In wasquith/lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

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)

Arguments

f	Nonexceedance probability (0 \le F \le 1).
para	The parameters from lmom2par or vec2par.

Value

Residual variance value for F.

Author(s)

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.
## Not run: 
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)

## End(Not run)

wasquith/lmomco documentation built on Nov. 13, 2024, 4:53 p.m.