ParetoQQ_der: Derivative plot of the Pareto QQ-plot

In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Derivative plot of the Pareto QQ-plot

Description

Computes the derivative plot of the Pareto QQ-plot. These values can be plotted as a function of the data or as a function of the tail parameter k.

Usage

ParetoQQ_der(data, k = FALSE, plot = TRUE, 
             main = "Derivative plot of Pareto QQ-plot", ...)

Arguments

data	Vector of n observations.
plot	Logical indicating if the derivative values should be plotted, default is TRUE.
k	Logical indicating if the derivative values are plotted as a function of the tail parameter k (k=TRUE) or as a function of the logarithm of the data (k=FALSE). Default is FALSE.
main	Title for the plot, default is "Derivative plot of Pareto QQ-plot".
...	Additional arguments for the plot function, see plot for more details.

Details

The derivative plot of a Pareto QQ-plot is

(k,H_{k,n})

or

(\log X_{n-k,n}, H_{k,n})

with H_{k,n} the Hill estimates.

See Section 4.1 of Albrecher et al. (2017) for more details.

Value

A list with following components:

xval	Vector of the x-values of the plot (k or \log X_{n-k,n}).
yval	Vector of the derivative values H_{k,n}.

Author(s)

Tom Reynkens.

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

ParetoQQ, Hill, MeanExcess, LognormalQQ_der, WeibullQQ_der

Examples

data(norwegianfire)

# Pareto QQ-plot for Norwegian Fire Insurance data for claims in 1976.
ParetoQQ(norwegianfire$size[norwegianfire$year==76])

# Derivate plot
ParetoQQ_der(norwegianfire$size[norwegianfire$year==76])

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