ReIns: genQQ – R documentation

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genQQ

Generalised quantile plot

Description

Computes the empirical quantiles of the UH scores of a data vector and the theoretical quantiles of the standard exponential distribution. These quantiles are then plotted in a generalised QQ-plot with the theoretical quantiles on the x-axis and the empirical quantiles on the y-axis.

Usage

genQQ(data, gamma, plot = TRUE, main = "Generalised QQ-plot", ...)

generalizedQQ(data, gamma, plot = TRUE, main = "Generalised QQ-plot", ...)

Arguments

`data`	Vector of n observations.
`gamma`	Vector of n-1 estimates for the EVI, typically Hill estimates are used.
`plot`	Logical indicating if the quantiles should be plotted in a generalised QQ-plot, default is `TRUE`.
`main`	Title for the plot, default is `"Generalised QQ-plot"`.
`...`	Additional arguments for the `plot` function, see `plot` for more details.

Details

The generalizedQQ function is the same function but with a different name for compatibility with the old S-Plus code.

The UH scores are defined as UH_{j,n}=X_{n-j,n}H_{j,n} with H_{j,n} the Hill estimates, but other positive estimates for the EVI can also be used. The appropriate positive estimates for the EVI need to be specified in gamma. The generalised QQ-plot then plots

(\log((n+1)/(k+1)), \log(X_{n-k,n}H_{k,n}))

for k=1,…,n-1.

See Section 4.2.2 of Albrecher et al. (2017) for more details.

Value

A list with following components:

`gqq.the`	Vector of the theoretical quantiles from a standard exponential distribution.
`gqq.emp`	Vector of the empirical quantiles from the logarithm of the UH scores.

Author(s)

Tom Reynkens based on S-Plus code from Yuri Goegebeur.

References

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.

Beirlant, J., Vynckier, P. and Teugels, J.L. (1996). "Excess Function and Estimation of the Extreme-value Index." Bernoulli, 2, 293–318.

Examples

data(soa)

# Compute Hill estimator
H <- Hill(soa$size[1:5000], plot=FALSE)$gamma

# Generalised QQ-plot
genQQ(soa$size[1:5000], gamma=H)

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