icParetoQQ {ReIns}

Pareto quantile plot for interval censored data

Description

Pareto QQ-plot adapted for interval censored data using the Turnbull estimator.

Usage

icParetoQQ(L, U = L, censored, trunclower = 0, truncupper = Inf, 
           plot = TRUE, main = "Pareto QQ-plot", ...)

Arguments

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 Inf (no upper truncation).

plot

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

main

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

...

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

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.

Value

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.

Author(s)

Tom Reynkens

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

See Also

cParetoQQ, ParetoQQ, icHill, Turnbull, icfit

Examples

# 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)