Pareto quantile plot for right censored data
Pareto QQ-plot adapted for right censored data.
cParetoQQ(data, censored, plot = TRUE, main = "Pareto QQ-plot", ...)
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 Pareto QQ-plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
The Pareto QQ-plot adapted for right censoring is given by
( -\log(1-F_{km}(Z_{j,n})), \log Z_{j,n} )
for j=1,…,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 Pareto QQ-plot but replaces the theoretical quantiles -\log(1-j/(n+1)) by -\log(1-F_{km}(Z_{j,n})).
This QQ-plot is only suitable for right censored data, use icParetoQQ for interval censored data.
A list with following components:
pqq.the |
Vector of the theoretical quantiles, see Details. |
pqq.emp |
Vector of the empirical quantiles from the log-transformed data. |
Tom Reynkens
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.
# 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) # Pareto QQ-plot adapted for right censoring cParetoQQ(Z, censored=censored)
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