icParetoQQ {ReIns} | R Documentation |
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.
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:
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.
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)