# LognormalQQ_der: Derivative plot of the log-normal QQ-plot In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

## Description

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

## Usage

 ```1 2``` ```LognormalQQ_der(data, k = FALSE, plot = TRUE, main = "Derivative plot of log-normal 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 log-normal QQ-plot"`. `...` Additional arguments for the `plot` function, see `plot` for more details.

## Details

The derivative plot of a log-normal QQ-plot is

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

or

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

with H_{k,n} the Hill estimates and

N_{k,n} = (n+1)/(k+1) φ(Φ^{-1}(a)) - Φ^{-1}(a).

Here is a=1-(k+1)/(n+1), φ the standard normal PDF and Φ the standard normal CDF.

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.

Tom Reynkens.

## References

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

`LognormalQQ`, `Hill`, `MeanExcess`, `ParetoQQ_der`, `WeibullQQ_der`

## Examples

 ```1 2 3 4 5 6 7``` ```data(norwegianfire) # Log-normal QQ-plot for Norwegian Fire Insurance data for claims in 1976. LognormalQQ(norwegianfire\$size[norwegianfire\$year==76]) # Derivate plot LognormalQQ_der(norwegianfire\$size[norwegianfire\$year==76]) ```

### Example output

```
```

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