Conditional Pareto quantile plot for right censored data
Conditional Pareto QQ-plot adapted for right censored data.
crParetoQQ(x, Xtilde, Ytilde, censored, h,
kernel = c("biweight", "normal", "uniform", "triangular", "epanechnikov"),
plot = TRUE, add = FALSE, main = "Pareto QQ-plot", type = "p", ...)x |
Value of the conditioning variable X at which to make the conditional Pareto QQ-plot. |
Xtilde |
Vector of length n containing the censored sample of the conditioning variable X. |
Ytilde |
Vector of length n containing the censored sample of the variable Y. |
censored |
A logical vector of length n indicating if an observation is censored. |
h |
Bandwidth of the non-parametric estimator for the conditional survival function ( |
kernel |
Kernel of the non-parametric estimator for the conditional survival function ( |
plot |
Logical indicating if the quantiles should be plotted in a Pareto QQ-plot, default is |
add |
Logical indicating if the quantiles should be added to an existing plot, default is |
main |
Title for the plot, default is |
type |
Type of the plot, default is |
... |
Additional arguments for the |
We construct a Pareto QQ-plot for Y conditional on X=x using the censored sample (\tilde{X}_i, \tilde{Y}_i), for i=1,…,n, where X and Y are censored at the same time. We assume that Y and the censoring variable are conditionally independent given X.
The conditional Pareto QQ-plot adapted for right censoring is given by
( -\log(1-\hat{F}_{Y|X}(\tilde{Y}_{j,n}|x)), \log \tilde{Y}_{j,n} )
for j=1,…,n-1,
with \tilde{Y}_{i,n} the i-th order statistic of the censored data and \hat{F}_{Y|X}(y|x) the non-parametric estimator for the conditional CDF of Akritas and Van Keilegom (2003), see crSurv.
See Section 4.4.3 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 Y data. |
Tom Reynkens
Akritas, M.G. and Van Keilegom, I. (2003). "Estimation of Bivariate and Marginal Distributions With Censored Data." Journal of the Royal Statistical Society: Series B, 65, 457–471.
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
# Set seed set.seed(29072016) # Pareto random sample Y <- rpareto(200, shape=2) # Censoring variable C <- rpareto(200, shape=1) # Observed (censored) sample of variable Y Ytilde <- pmin(Y, C) # Censoring indicator censored <- (Y>C) # Conditioning variable X <- seq(1, 10, length.out=length(Y)) # Observed (censored) sample of conditioning variable Xtilde <- X Xtilde[censored] <- X[censored] - runif(sum(censored), 0, 1) # Conditional Pareto QQ-plot crParetoQQ(x=1, Xtilde=Xtilde, Ytilde=Ytilde, censored=censored, h=2) # Plot Hill-type estimates crHill(x=1, Xtilde, Ytilde, censored, h=2, plot=TRUE)
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