LognormalQQ_der function

Derivative plot of the log-normal QQ-plot

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 $k$.

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

or

with $H_{k,n}$ the Hill estimates and

Here is $a=1-(k+1)/(n+1)$, $\phi$ the standard normal PDF and $\Phi$ the standard normal CDF.

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

Returns

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.

References

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

Author(s)

Tom Reynkens.

See Also

LognormalQQ, Hill, MeanExcess, ParetoQQ_der, WeibullQQ_der

Examples

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])