Pareto quantile plot for interval censored data
Pareto QQ-plot adapted for interval censored data using the Turnbull estimator.
icParetoQQ(L, U = L, censored, trunclower = 0, truncupper = Inf,
plot = TRUE, main = "Pareto QQ-plot", ...)L |
Vector of length n with the lower boundaries of the intervals for interval censored data or the observed data for right censored data. |
U |
Vector of length n with the upper boundaries of the intervals. |
censored |
A logical vector of length n indicating if an observation is censored. |
trunclower |
Lower truncation point. Default is 0. |
truncupper |
Upper truncation point. Default is |
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 interval censoring is given by
( -\log(1-F^{TB}(x_{j,n})), \log x_{j,n} )
for j=1,…,n-1, where \hat{F}^{TB} is the Turnbull estimator for the CDF and x_{i,n}=\hat{Q}^{TB}(i/(n+1)) with \hat{Q}^{TB}(p) the empirical quantile function corresponding to the Turnbull estimator.
Right censored data should be entered as L=l and U=truncupper, and left censored data should be entered as L=trunclower and U=u.
If the interval package is installed, the icfit function is used to compute the Turnbull estimator. Otherwise, survfit.formula from survival is used.
See Section 4.3 in Albrecher et al. (2017) for more details.
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
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
# 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) # Right boundary U <- Z U[censored] <- Inf # Pareto QQ-plot adapted for interval censoring icParetoQQ(Z, U, censored) # Pareto QQ-plot adapted for right censoring cParetoQQ(Z, censored)
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