Weibull quantile plot
Computes the empirical quantiles of the log-transform of a data vector and the theoretical quantiles of the standard Weibull distribution. These quantiles are then plotted in a Weibull QQ-plot with the theoretical quantiles on the x-axis and the empirical quantiles on the y-axis.
WeibullQQ(data, plot = TRUE, main = "Weibull QQ-plot", ...)
data |
Vector of n observations. |
plot |
Logical indicating if the quantiles should be plotted in a Weibull QQ-plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
The Weibull QQ-plot is given by
(\log(-\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:
wqq.the |
Vector of the theoretical quantiles from a standard Weibull distribution. |
wqq.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.
data(norwegianfire) # Weibull QQ-plot for Norwegian Fire Insurance data for claims in 1976. WeibullQQ(norwegianfire$size[norwegianfire$year==76]) # Derivative of Weibull QQ-plot for Norwegian Fire Insurance data for claims in 1976. WeibullQQ_der(norwegianfire$size[norwegianfire$year==76])
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