quagov: Quantile Function of the Govindarajulu Distribution

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

Quantile Function of the Govindarajulu Distribution

Description

This function computes the quantiles of the Govindarajulu distribution given parameters (\xi, \alpha, and \beta) computed by pargov. The quantile function is

x(F) = \xi + \alpha[(\beta+1)F^\beta - \beta F^{\beta+1}] \mbox{,}

where x(F) is the quantile for nonexceedance probability F, \xi is location parameter, \alpha is a scale parameter, and \beta is a shape parameter.

Usage

quagov(f, para, paracheck=TRUE)

Arguments

f	Nonexceedance probability (0 \le F \le 1).
para	The parameters from pargov or similar.
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 for nonexceedance probability F.

Author(s)

W.H. Asquith

References

Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton.

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

Nair, N.U., Sankaran, P.G., and Vineshkumar, B., 2012, The Govindarajulu distribution—Some Properties and applications: Communications in Statistics, Theory and Methods, 41(24), 4391–4406.

See Also

cdfgov, pdfgov, lmomgov, pargov

Examples

lmr <- lmoms(c(123,34,4,654,37,78))
quagov(0.5,pargov(lmr))
## Not run: 
lmr <- lmoms(c(3, 0.05, 1.6, 1.37, 0.57, 0.36, 2.2));
par <- pargov(lmr)# LMRQ said to have a linear mean residual quantile function.
# Let us have a look.
F <- c(0,nonexceeds(),1)
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 how the conditional mean attaches to the parent at F=1, but it does not
# attached at F=0 because of the none zero origin.
cmlmomco(0,par)           # 1.307143 # expected life given birth only
lmomgov(par)$lambdas[1]   # 1.307143 # expected life of the parent distribution
rmlmomco(0, par)          # 1.288989 # residual life given birth only
qlmomco(0, par)           # 0.018153 # instantaneous life given birth
# Note: qlmomco(0,par) + rmlmomco(0,par) is the E[lifetime], but rmlmomco()
# is the RESIDUAL MEAN LIFE.

## End(Not run)

lmomco documentation built on May 29, 2024, 10:06 a.m.