LognormalQQ function

Log-normal quantile plot

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.

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

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.

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

for $i=1,\ldots,n,$ where $\Phi$ is the standard normal CDF.

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

Returns

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.

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.

Author(s)

Tom Reynkens.

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])