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", ...)
data |
Vector of n observations. |
plot |
Logical indicating if the quantiles should be plotted in a log-normal QQ-plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
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
(Φ^{-1}(i/(n+1)), \log(X_{i,n}) )
for i=1,…,n, where Φ is the standard normal CDF.
See Section 4.1 of Albrecher et al. (2017) for more details.
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. |
Tom Reynkens.
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.
data(norwegianfire) # Log-normal QQ-plot for Norwegian Fire Insurance data for claims in 1976. LognormalQQ(norwegianfire$size[norwegianfire$year==76])
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.