# MeanExcess: Mean excess function In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

 MeanExcess R Documentation

## 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.

### 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.

### 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.

### Author(s)

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

### 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.

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)



ReIns documentation built on March 31, 2023, 8:09 p.m.