ReIns: WeibullQQ_der – R documentation

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WeibullQQ_der

Derivative plot of the Weibull QQ-plot

Description

Computes the derivative plot of the Weibull QQ-plot. These values can be plotted as a function of the data or as a function of the tail parameter k.

Usage

WeibullQQ_der(data, k = FALSE, plot = TRUE, 
              main = "Derivative plot of Weibull QQ-plot", ...)

Arguments

`data`	Vector of n observations.
`plot`	Logical indicating if the derivative values should be plotted, default is `TRUE`.
`k`	Logical indicating if the derivative values are plotted as a function of the tail parameter k (`k=TRUE`) or as a function of the logarithm of the data (`k=FALSE`). Default is `FALSE`.
`main`	Title for the plot, default is `"Derivative plot of Weibull QQ-plot"`.
`...`	Additional arguments for the `plot` function, see `plot` for more details.

Details

The derivative plot of a Weibull QQ-plot is

(k, H_{k,n}/W_{k,n})

(\log X_{n-k,n}, H_{k,n}/W_{k,n})

with H_{k,n} the Hill estimates and

W_{k,n}=1/k∑_{j=1}^k \log(\log((n+1)/j)) - \log(\log((n+1)/(k+1))).

See Section 4.1 of Albrecher et al. (2017) for more details.

Value

A list with following components:

`xval`	Vector of the x-values of the plot (k or \log X_{n-k,n}).
`yval`	Vector of the derivative values.

Author(s)

Tom Reynkens.

References

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

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])

ReIns

Functions from "Reinsurance: Actuarial and Statistical Aspects"

v1.0.10

GPL (>= 2)

Authors

Tom Reynkens [aut, cre] (<https://orcid.org/0000-0002-5516-5107>), Roel Verbelen [aut] (R code for Mixed Erlang distribution, <https://orcid.org/0000-0002-2347-9240>), Anastasios Bardoutsos [ctb] (Original R code for cEPD estimator), Dries Cornilly [ctb] (Original R code for EVT estimators for truncated data), Yuri Goegebeur [ctb] (Original S-Plus code for basic EVT estimators), Klaus Herrmann [ctb] (Original R code for GPD estimator)

Initial release

2020-05-16