## risk.PotTail


A peaks-over-threshold tail: draws above a threshold modelled by a


Usage


``` python
risk.PotTail()
```


fitted generalized Pareto distribution, for VaR and TVaR beyond the draws.

Make one with `PotTail.fit(draws, level)`, which takes the threshold at the empirical `level` quantile.


## Examples

``` python
>>> from prospicio.distributions import Lognormal, Sampled
>>> from prospicio.risk import PotTail
>>> d = Lognormal(0.0, 1.0)
>>> s = Sampled([d.quantile((i - 0.5) / 100_000) for i in range(1, 100_001)])
>>> tail = PotTail.fit(s, 0.95)
>>> abs(tail.var(0.999) / d.quantile(0.999) - 1) < 0.02
```

True


## Attributes

| Name | Description |
|----|----|
| [gpd](#gpd) | The fitted GPD for the exceedances. |
| [p_exceed](#p_exceed) | Share of draws above the threshold. |
| [threshold](#threshold) | Threshold `u`. |

------------------------------------------------------------------------


#### gpd


The fitted GPD for the exceedances.


`gpd: Gpd`


------------------------------------------------------------------------


#### p_exceed


Share of draws above the threshold.


`p_exceed: float`


------------------------------------------------------------------------


#### threshold


Threshold `u`.


`threshold: float`


## Methods

| Name | Description |
|----|----|
| [fit()](#fit) | Fits a tail to the draws above their empirical `level` quantile. |
| [tvar()](#tvar) | TVaR at `p >= 1 - p_exceed`; infinite when `xi >= 1`. |
| [var()](#var) | VaR at `p >= 1 - p_exceed`. |

------------------------------------------------------------------------


#### fit()


Fits a tail to the draws above their empirical `level` quantile.


Usage


``` python
fit(draws, level)
```


##### Parameters


`draws: Sampled`  

`level: float`  
For example 0.95 for the top 5%.


##### Returns


`PotTail`  


------------------------------------------------------------------------


#### tvar()


TVaR at `p >= 1 - p_exceed`; infinite when `xi >= 1`.


Usage


``` python
tvar(p)
```


##### Parameters


`p: float`  


##### Returns


`float`  


------------------------------------------------------------------------


#### var()


VaR at `p >= 1 - p_exceed`.


Usage


``` python
var(p)
```


##### Parameters


`p: float`  


##### Returns


`float`