tea (version 1.1)

qqestplot: QQ-Estimator-Plot

Description

Plots the QQ-Estimator against the upper order statistics

Usage

qqestplot(data, kmin = 5, conf.int = FALSE)

Arguments

data

vector of sample data

kmin

gives the minimal k for which the graph is plotted. Default ist set to kmin=5

conf.int

logical. If FALSE (default) no confidence intervals are plotted

Value

The plot shows the values of the QQ-Estimator with respect to k. See references for more information.

Details

The QQ-Estimator is a Tail Index Estimator based on regression diagnostics. Assuming a Pareto tail behaviour of the data at hand a QQ-Plot of the theoretical quantiles of an exponential distribution against the empirical quantiles of the log-data should lead to a straight line above some unknown upper order statistic k. The slope of this line is an estimator for the tail index. Computing this estimator via linear regression for every k the plot should stabilize for the correct number of upper order statistics, denoted k0 here.

References

Kratz, M. and Resnick, S.I. (1996). The QQ-estimator and heavy tails. Stochastic Models, 12(4), 699--724.

Examples

# NOT RUN {
data(danish)
qqestplot(danish)
# }