risk.Gpd
The generalized Pareto distribution, as SciPy’s
Usage
risk.Gpd()genpareto(c=xi, scale=beta).
P(X > x) = (1 + xi x / beta)**(-1 / xi) for x >= 0.
Parameters
xi: float-
Shape; moments of order
1 / xiand above are infinite. beta: float- Scale, positive.
Examples
>>> from prospicio.risk import Gpd
>>> g = Gpd(0.5, 2.0)
>>> g.mean()4.0
>>> fit = Gpd.fit([g.quantile((i - 0.5) / 1000) for i in range(1, 1001)])
>>> round(fit.xi, 2), round(fit.beta, 2)(0.5, 2.0)
Attributes
| Name | Description |
|---|---|
| beta | Scale. |
| xi | Shape. |
beta
Scale.
beta: float
xi
Shape.
xi: float
Methods
| Name | Description |
|---|---|
| cdf() | Distribution function. |
| fit() | Maximum likelihood fit to exceedances (values over a threshold, |
| mean() |
Mean, beta / (1 - xi); infinite for xi >= 1.
|
| quantile() | Quantile function. |
cdf()
Distribution function.
Usage
cdf(x)Parameters
x: float
Returns
float
fit()
Maximum likelihood fit to exceedances (values over a threshold,
Usage
fit(exceedances)minus the threshold).
Parameters
exceedances: list of float- At least 3, non-negative, not all equal.
Returns
Gpd
mean()
Mean, beta / (1 - xi); infinite for xi >= 1.
Usage
mean()quantile()
Quantile function.
Usage
quantile(p)Parameters
p: float
Returns
float