icParetoQQ function

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", ...)

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

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.

Returns

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.

References

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

Author(s)

Tom Reynkens

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)