cGPD: GPD-ML estimator for right censored data

In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

GPD-ML estimator for right censored data

Description

Computes ML estimates of fitting GPD to peaks over a threshold adapted for right censoring.

Usage

cGPDmle(data, censored, start = c(0.1,1), warnings = FALSE, logk = FALSE, 
        plot = FALSE, add = FALSE, main = "POT estimates of the EVI", ...)
      
cPOT(data, censored, start = c(0.1,1), warnings = FALSE, logk = FALSE, 
     plot = FALSE, add = FALSE, main = "POT estimates of the EVI", ...)

Arguments

data	Vector of n observations.
censored	A logical vector of length n indicating if an observation is censored.
start	Vector of length 2 containing the starting values for the optimisation. The first element is the starting value for the estimator of \gamma_1 and the second element is the starting value for the estimator of \sigma_1. Default is c(0.1,1).
warnings	Logical indicating if possible warnings from the optimisation function are shown, default is FALSE.
logk	Logical indicating if the estimates are plotted as a function of \log(k) (logk=TRUE) or as a function of k. Default is FALSE.
plot	Logical indicating if the estimates of \gamma_1 should be plotted as a function of k, default is FALSE.
add	Logical indicating if the estimates of \gamma_1 should be added to an existing plot, default is FALSE.
main	Title for the plot, default is "POT estimates of the EVI".
...	Additional arguments for the plot function, see plot for more details.

Details

The GPD-MLE estimator for the EVI adapted for right censored data is equal to the ordinary GPD-MLE estimator for the EVI divided by the proportion of the k largest observations that is non-censored. The estimates for \sigma are the ordinary GPD-MLE estimates for \sigma.

This estimator is only suitable for right censored data.

cPOT is the same function but with a different name for compatibility with POT.

Value

A list with following components:

k	Vector of the values of the tail parameter k.
gamma1	Vector of the corresponding MLE estimates for the \gamma_1 parameter of the GPD.
sigma1	Vector of the corresponding MLE estimates for the \sigma_1 parameter of the GPD.

Author(s)

Tom Reynkens

References

Einmahl, J.H.J., Fils-Villetard, A. and Guillou, A. (2008). "Statistics of Extremes Under Random Censoring." Bernoulli, 14, 207–227.

See Also

GPDmle, cProbGPD, cQuantGPD, cEPD

Examples

# 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)

# GPD-ML estimator adapted for right censoring
cpot <- cGPDmle(Z, censored=censored, plot=TRUE)

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.