ReIns (version 1.0.10)

ExpQQ: Exponential quantile plot

Description

Computes the empirical quantiles of a data vector and the theoretical quantiles of the standard exponential distribution. These quantiles are then plotted in an exponential QQ-plot with the theoretical quantiles on the \(x\)-axis and the empirical quantiles on the \(y\)-axis.

Usage

ExpQQ(data, plot = TRUE, main = "Exponential QQ-plot", ...)

Value

A list with following components:

eqq.the

Vector of the theoretical quantiles from a standard exponential distribution.

eqq.emp

Vector of the empirical quantiles from the data.

Arguments

data

Vector of \(n\) observations.

plot

Logical indicating if the quantiles should be plotted in an Exponential QQ-plot, default is TRUE.

main

Title for the plot, default is "Exponential QQ-plot".

...

Additional arguments for the plot function, see plot for more details.

Author

Tom Reynkens based on S-Plus code from Yuri Goegebeur.

Details

The exponential QQ-plot is defined as $$( -\log(1-i/(n+1)), X_{i,n} )$$ for \(i=1,...,n,\) with \(X_{i,n}\) the \(i\)-th order statistic of the data.

Note that the mean excess plot is the derivative plot of the Exponential QQ-plot.

See Section 4.1 of Albrecher et al. (2017) for more details.

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.

See Also

MeanExcess, LognormalQQ, ParetoQQ, WeibullQQ

Examples

Run this code
data(norwegianfire)

# Exponential QQ-plot for Norwegian Fire Insurance data for claims in 1976.
ExpQQ(norwegianfire$size[norwegianfire$year==76])

# Pareto QQ-plot for Norwegian Fire Insurance data for claims in 1976.
ParetoQQ(norwegianfire$size[norwegianfire$year==76])

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