LognormalQQ_der: Derivative plot of the log-normal QQ-plot

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/QQplots.R

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.

Author(s)

Tom Reynkens.

References

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

See Also

LognormalQQ, Hill, MeanExcess, ParetoQQ_der, WeibullQQ_der

Examples

1
2
3
4
5
6
7
data(norwegianfire)

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

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

Example output



ReIns documentation built on July 2, 2020, 4:03 a.m.