ExpQQ: Exponential quantile plot In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

 ExpQQ R Documentation

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", ...)
``````

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.

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.

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.

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.

`MeanExcess`, `LognormalQQ`, `ParetoQQ`, `WeibullQQ`

Examples

``````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])
``````

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.