# Quant2o: Second order refined Weissman estimator of extreme quantiles... In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

## Description

Compute second order refined Weissman estimator of extreme quantiles Q(1-p) using the quantile view.

## Usage

 ```1 2 3 4 5``` ```Quant.2oQV(data, gamma, b, beta, p, plot = FALSE, add = FALSE, main = "Estimates of extreme quantile", ...) Weissman.q.2oQV(data, gamma, b, beta, p, plot = FALSE, add = FALSE, main = "Estimates of extreme quantile", ...) ```

## Arguments

 `data` Vector of n observations. `gamma` Vector of n-1 estimates for the EVI obtained from `Hill.2oQV`. `b` Vector of n-1 estimates for b obtained from `Hill.2oQV`. `beta` Vector of n-1 estimates for β obtained from `Hill.2oQV`. `p` The exceedance probability of the quantile (we estimate Q(1-p) for p small). `plot` Logical indicating if the estimates should be plotted as a function of k, default is `FALSE`. `add` Logical indicating if the estimates should be added to an existing plot, default is `FALSE`. `main` Title for the plot, default is `"Estimates of extreme quantile"`. `...` Additional arguments for the `plot` function, see `plot` for more details.

## Details

See Section 4.2.1 of Albrecher et al. (2017) for more details.

`Weissman.q.2oQV` is the same function but with a different name for compatibility with the old `S-Plus` code.

## Value

A list with following components:

 `k` Vector of the values of the tail parameter k. `Q` Vector of the corresponding quantile estimates. `p` The used exceedance probability.

## 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.

`Quant`, `Hill.2oQV`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```data(soa) # Look at last 500 observations of SOA data SOAdata <- sort(soa\$size)[length(soa\$size)-(0:499)] # Hill estimator H <- Hill(SOAdata) # Bias-reduced estimator (QV) H_QV <- Hill.2oQV(SOAdata) # Exceedance probability p <- 10^(-5) # Weissman estimator Quant(SOAdata, gamma=H\$gamma, p=p, plot=TRUE) # Second order Weissman estimator (QV) Quant.2oQV(SOAdata, gamma=H_QV\$gamma, beta=H_QV\$beta, b=H_QV\$b, p=p, add=TRUE, lty=2) ```

### Example output ```
```

ReIns documentation built on July 2, 2020, 4:03 a.m.