ReIns (version 1.0.10)

LognormalQQ: Log-normal quantile plot

Description

Computes the empirical quantiles of the log-transform of a data vector and the theoretical quantiles of the standard normal distribution. These quantiles are then plotted in a log-normal QQ-plot with the theoretical quantiles on the \(x\)-axis and the empirical quantiles on the \(y\)-axis.

Usage

LognormalQQ(data, plot = TRUE, main = "Log-normal QQ-plot", ...)

Value

A list with following components:

lnqq.the

Vector of the theoretical quantiles from a standard normal distribution.

lnqq.emp

Vector of the empirical quantiles from the log-transformed data.

Arguments

data

Vector of \(n\) observations.

plot

Logical indicating if the quantiles should be plotted in a log-normal QQ-plot, default is TRUE.

main

Title for the plot, default is "Log-normal QQ-plot".

...

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

Author

Tom Reynkens.

Details

By definition, a log-transformed log-normal random variable is normally distributed. We can thus obtain a log-normal QQ-plot from a normal QQ-plot by replacing the empirical quantiles of the data vector by the empirical quantiles from the log-transformed data. We hence plot $$(\Phi^{-1}(i/(n+1)), \log(X_{i,n}) )$$ for \(i=1,\ldots,n,\) where \(\Phi\) is the standard normal CDF.

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

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

ExpQQ, ParetoQQ, WeibullQQ

Examples

data(norwegianfire)

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