ReIns (version 1.0.7)

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", ...)

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.

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.

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

# NOT RUN {
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)

# }