cMoment function

MOM estimator for right censored data

Computes the Method of Moment estimates adapted for right censored data.

cMoment(data, censored, logk = FALSE, plot = FALSE, add = FALSE, 
        main = "Moment estimates of the EVI", ...)

Arguments

• data: Vector of $n$ observations.
• censored: A logical vector of length $n$ indicating if an observation is censored.
• 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 "Moment estimates of the EVI".
• ...: Additional arguments for the plot function, see plot for more details.

Details

The moment estimator adapted for right censored data is equal to the ordinary moment estimator divided by the proportion of the $k$ largest observations that is non-censored.

This estimator is only suitable for right censored data.

Returns

A list with following components: - k: Vector of the values of the tail parameter $k$.

• gamma1: Vector of the corresponding moment estimates.

References

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

Author(s)

Tom Reynkens

See Also

Moment, cProbMOM, cQuantMOM

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)

# Moment estimator adapted for right censoring
cmom <- cMoment(Z, censored=censored, plot=TRUE)