# cQuant: Estimator of large quantiles using censored Hill In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

## Description

Computes estimates of large quantiles Q(1-p) using the estimates for the EVI obtained from the Hill estimator adapted for right censoring.

## Usage

 1 2 cQuant(data, censored, gamma1, p, plot = FALSE, add = FALSE, main = "Estimates of extreme quantile", ...) 

## Arguments

 data Vector of n observations. censored A logical vector of length n indicating if an observation is censored. gamma1 Vector of n-1 estimates for the EVI obtained from cHill. p The exceedance probability of the quantile (we estimate Q(1-p) for p small). plot Logical indicating if the estimates should be plotted as a function of k, default is FALSE. add Logical indicating if the estimates should be added to an existing plot, default is FALSE. main Title for the plot, default is "Estimates of extreme quantile". ... Additional arguments for the plot function, see plot for more details.

## Details

The quantile is estimated as

\hat{Q}(1-p)=Z_{n-k,n} \times ( (1-km)/p)^{H_{k,n}^c}

with Z_{i,n} the i-th order statistic of the data, H_{k,n}^c the Hill estimator adapted for right censoring and km the Kaplan-Meier estimator for the CDF evaluated in Z_{n-k,n}.

## Value

A list with following components:

 k Vector of the values of the tail parameter k. Q Vector of the corresponding quantile estimates. p The used exceedance probability.

Tom Reynkens.

## References

Beirlant, J., Guillou, A., Dierckx, G. and Fils-Villetard, A. (2007). "Estimation of the Extreme Value Index and Extreme Quantiles Under Random Censoring." Extremes, 10, 151–174.

cHill, cProb, Quant, KaplanMeier

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 # Set seed set.seed(29072016) # 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) # Hill estimator adapted for right censoring chill <- cHill(Z, censored=censored, plot=TRUE) # Large quantile p <- 10^(-4) cQuant(Z, gamma1=chill\$gamma, censored=censored, p=p, plot=TRUE) 

### Example output




ReIns documentation built on July 2, 2020, 4:03 a.m.