icParetoQQ: Pareto quantile plot for interval censored data

View source: R/IntervalCensoring.R

icParetoQQR Documentation

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", ...)



Vector of length n with the lower boundaries of the intervals for interval censored data or the observed data for right censored data.


Vector of length n with the upper boundaries of the intervals.


A logical vector of length n indicating if an observation is censored.


Lower truncation point. Default is 0.


Upper truncation point. Default is Inf (no upper truncation).


Logical indicating if the quantiles should be plotted in a Pareto QQ-plot, default is TRUE.


Title for the plot, default is "Pareto QQ-plot".


Additional arguments for the plot function, see plot for more details.


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,\ldots,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.

Use ParetoQQ for non-censored data or cParetoQQ for right censored data.

See Section 4.3 in Albrecher et al. (2017) for more details.


A list with following components:


Vector of the theoretical quantiles, see Details.


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.

See Also

cParetoQQ, ParetoQQ, icHill, Turnbull, icfit


# 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)

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