ReIns (version 1.0.10)

MeanExcess: Mean excess function

Description

Computes the mean excess values for a vector of observations. These mean excess values can then be plotted as a function of the data or as a function of the tail parameter \(k\).

Usage

MeanExcess(data, plot = TRUE, k = FALSE, main = "Mean excess plot", ...)

Value

A list with following components:

k

Vector of the values of the tail parameter k.

X

Vector of the order statistics data[n-k] corresponding to the tail parameters in k.

e

Vector of the mean excess values corresponding to the tail parameters in k.

Arguments

data

Vector of \(n\) observations.

plot

Logical indicating if the mean excess values should be plotted in a mean excess plot, default is TRUE.

k

Logical indicating if the mean excess scores are plotted as a function of the tail parameter \(k\) (k=TRUE) or as a function of the data (k=FALSE). Default is FALSE.

main

Title for the plot, default is "Mean excess 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 mean excess plot is $$(k,e_{k,n})$$ or $$(X_{n-k,n}, e_{k,n})$$ with $$e_{k,n}=1/k\sum_{j=1}^k X_{n-j+1,n}-X_{n-k,n}.$$

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

ExpQQ, LognormalQQ_der, ParetoQQ_der, WeibullQQ_der

Examples

data(norwegianfire)

# Mean excess plots for Norwegian Fire Insurance data for claims in 1976.

# Mean excess values as a function of k
MeanExcess(norwegianfire$size[norwegianfire$year==76], k=TRUE)

# Mean excess values as a function of the data
MeanExcess(norwegianfire$size[norwegianfire$year==76], k=FALSE)