ReIns (version 1.0.7)

WeibullQQ: Weibull quantile plot

Description

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.

Usage

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.

Value

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.

Details

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.

References

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

See Also

WeibullQQ_der, ExpQQ, LognormalQQ, ParetoQQ

Examples

# NOT RUN {
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])
# }