cLognormalQQ function

Log-normal quantile plot for right censored data

Log-normal QQ-plot adapted for right censored data.

cLognormalQQ(data, censored, plot = TRUE, main = "Log-normal 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 log-normal QQ-plot, default is TRUE.
• main: Title for the plot, default is "Log-normal QQ-plot".
• ...: Additional arguments for the plot function, see plot for more details.

Details

The log-normal QQ-plot adapted for right censoring is given by

for $j=1,\ldots,n-1,$

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

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.

Returns

A list with following components: - lqq.the: Vector of the theoretical quantiles, see Details.

• lqq.emp: Vector of the empirical quantiles from the log-transformed data.

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.

Author(s)

Tom Reynkens

See Also

LognormalQQ, cExpQQ, cParetoQQ, cWeibullQQ, 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)

# Log-normal QQ-plot adapted for right censoring
cLognormalQQ(Z, censored=censored)