WeibullQQ_der {ReIns}

Derivative plot of the Weibull QQ-plot

Description

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

Usage

WeibullQQ_der(data, k = FALSE, plot = TRUE, 
              main = "Derivative plot of Weibull 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 Weibull QQ-plot".

...

Additional arguments for the plot function, see plot for more details.

Details

The derivative plot of a Weibull QQ-plot is

(k, H_{k,n}/W_{k,n})

or

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

with H_{k,n} the Hill estimates and

W_{k,n}=1/k\sum_{j=1}^k \log(\log((n+1)/j)) - \log(\log((n+1)/(k+1))).

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.

Author(s)

Tom Reynkens.

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

See Also

WeibullQQ, Hill, MeanExcess, LognormalQQ_der, ParetoQQ_der

Examples

data(norwegianfire)

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

# Derivative of Weibull QQ-plot for Norwegian Fire Insurance data for claims in 1976.
WeibullQQ_der(norwegianfire$size[norwegianfire$year==76])