ReIns (version 1.0.7)

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", ...)

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.

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.

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

# NOT RUN {
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])
# }