WeibullQQ function

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", ...)

Arguments

• data: Vector of $n$ observations.
• plot: Logical indicating if the quantiles should be plotted in a Weibull QQ-plot, default is TRUE.
• main: Title for the plot, default is "Weibull QQ-plot".
• ...: Additional arguments for the plot function, see plot for more details.

Details

The Weibull QQ-plot is given by

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.

Returns

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.

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Author(s)

Tom Reynkens.

See Also

WeibullQQ_der, ExpQQ, LognormalQQ, ParetoQQ

Examples

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])