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", ...)
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.
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.
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.
# NOT RUN {data(norwegianfire)
# Log-normal QQ-plot for Norwegian Fire Insurance data for claims in 1976.LognormalQQ(norwegianfire$size[norwegianfire$year==76])
# }