Pareto quantile plot
Computes the empirical quantiles of the log-transform of a data vector and the theoretical quantiles of the standard exponential distribution. These quantiles are then plotted in a Pareto QQ-plot with the theoretical quantiles on the x-axis and the empirical quantiles on the y-axis.
ParetoQQ(data, plot = TRUE, main = "Pareto QQ-plot", ...)
data |
Vector of n observations. |
plot |
Logical indicating if the quantiles should be plotted in a Pareto QQ-plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
It can be easily seen that a log-transformed Pareto random variable is exponentially distributed. We can hence obtain a Pareto QQ-plot from an exponential QQ-plot by replacing the empirical quantiles from the data vector by the empirical quantiles from the log-transformed data. We hence plot
( -\log(1-i/(n+1)), \log X_{i,n} )
for i=1,...,n, with X_{i,n} the i-th order statistic of the data.
See Section 4.1 of Albrecher et al. (2017) for more details.
A list with following components:
pqq.the |
Vector of the theoretical quantiles from a standard exponential distribution. |
pqq.emp |
Vector of the empirical quantiles from the log-transformed data. |
Tom Reynkens based on S-Plus code from Yuri Goegebeur.
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) # Exponential QQ-plot for Norwegian Fire Insurance data for claims in 1976. ExpQQ(norwegianfire$size[norwegianfire$year==76]) # Pareto QQ-plot for Norwegian Fire Insurance data for claims in 1976. ParetoQQ(norwegianfire$size[norwegianfire$year==76])
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