# genQQ: Generalised quantile plot In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

 genQQ R Documentation

## 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,\ldots,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.

`ParetoQQ`, `Hill`

### 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 documentation built on Nov. 3, 2023, 5:08 p.m.