LognormalQQ_der: Derivative plot of the log-normal QQ-plot In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Description

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

Usage

 1 2 LognormalQQ_der(data, k = FALSE, plot = TRUE, main = "Derivative plot of log-normal 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 log-normal QQ-plot". ... Additional arguments for the plot function, see plot for more details.

Details

The derivative plot of a log-normal QQ-plot is

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

or

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

with H_{k,n} the Hill estimates and

N_{k,n} = (n+1)/(k+1) φ(Φ^{-1}(a)) - Φ^{-1}(a).

Here is a=1-(k+1)/(n+1), φ the standard normal PDF and Φ the standard normal CDF.

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.

Tom Reynkens.

References

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