cWeibullQQ: Weibull quantile plot for right censored data

In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Weibull quantile plot for right censored data

Description

Weibull QQ-plot adapted for right censored data.

Usage

cWeibullQQ(data, censored, plot = TRUE, main = "Weibull QQ-plot", ...)

Arguments

data	Vector of n observations.
censored	A logical vector of length n indicating if an observation is censored.
plot	Logical indicating if the quantiles should be plotted in a Weibull QQ-plot, default is TRUE.
main	Title for the plot, default is "Weibull QQ-plot".
...	Additional arguments for the plot function, see plot for more details.

Details

The Weibull QQ-plot adapted for right censoring is given by

( \log(-\log(1-F_{km}(Z_{j,n}))), \log(Z_{j,n}) )

for j=1,\ldots,n-1, with Z_{i,n} the i-th order statistic of the data and F_{km} the Kaplan-Meier estimator for the CDF. Hence, it has the same empirical quantiles as an ordinary Weibull QQ-plot but replaces the theoretical quantiles \log(-\log(1-j/(n+1))) by \log(-\log(1-F_{km}(Z_{j,n}))).

This QQ-plot is only suitable for right censored data.

In Beirlant et al. (2007), only a Pareto QQ-plot adapted for right-censored data is proposed. This QQ-plot is constructed using the same ideas, but is not described in the paper.

Value

A list with following components:

wqq.the	Vector of the theoretical quantiles, see Details.
wqq.emp	Vector of the empirical quantiles from the log-transformed data.

Author(s)

Tom Reynkens

References

Beirlant, J., Guillou, A., Dierckx, G. and Fils-Villetard, A. (2007). "Estimation of the Extreme Value Index and Extreme Quantiles Under Random Censoring." Extremes, 10, 151–174.

See Also

WeibullQQ, cExpQQ, cLognormalQQ, cParetoQQ, KaplanMeier

Examples

# Set seed
set.seed(29072016)

# Pareto random sample
X <- rpareto(500, shape=2)

# Censoring variable
Y <- rpareto(500, shape=1)

# Observed sample
Z <- pmin(X, Y)

# Censoring indicator
censored <- (X>Y)

# Weibull QQ-plot adapted for right censoring
cWeibullQQ(Z, censored=censored)

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.