distributions.Gamma

Gamma distribution with shape alpha and scale theta: mean

Usage

distributions.Gamma()

alpha * theta, variance alpha * theta**2.

Parameters

shape: float
scale: float

Raises

ValueError
If a parameter is not finite and positive.

Examples

>>> from prospicio.distributions import Gamma
>>> g = Gamma.from_mean_cv(1000.0, 0.5)
>>> g.shape, round(g.std(), 9)

(4.0, 500.0)

Attributes

Name Description
scale Scale theta.
shape Shape alpha.

scale

Scale theta.

scale: float

shape

Shape alpha.

shape: float

Methods

Name Description
cdf() Distribution function P(X <= x).
from_mean_cv() Gamma with the given mean and coefficient of variation.
from_mean_dispersion() Gamma with mean mu and GLM dispersion phi (variance
layer() Expected loss to the layer limit xs attachment.
layer_second_moment() Second moment of the loss to the layer limit xs
layer_variance() Variance of the loss to the layer limit xs attachment.
lev() Limited expected value E[min(X, limit)].
ln_pdf() Log density at x.
mean() Mean of the distribution (inf if it does not exist).
quantile() Quantile: the smallest x with P(X <= x) >= p.
sample() n draws from stream stream of the generator keyed by
std() Standard deviation of the distribution.
stop_loss() Expected excess over a retention, E[max(X - retention, 0)].
survival() Survival function P(X > x), accurate far into the tail.
variance() Variance of the distribution (inf if it does not exist).

cdf()

Distribution function P(X <= x).

Usage

cdf(x)
Parameters
x: float
Returns
float

from_mean_cv()

Gamma with the given mean and coefficient of variation.

Usage

from_mean_cv(mean, cv)
Parameters
mean: float
cv: float
Returns
Gamma

from_mean_dispersion()

Gamma with mean mu and GLM dispersion phi (variance

Usage

from_mean_dispersion(mean, dispersion)

phi * mu**2): shape 1 / phi.

Parameters
mean: float
dispersion: float
Returns
Gamma

layer()

Expected loss to the layer limit xs attachment.

Usage

layer(limit, attachment)
Parameters
limit: float

inf for an unlimited layer.

attachment: float
Returns
float

layer_second_moment()

Second moment of the loss to the layer limit xs

Usage

layer_second_moment(limit, attachment)

attachment.

Parameters
limit: float
attachment: float
Returns
float

layer_variance()

Variance of the loss to the layer limit xs attachment.

Usage

layer_variance(limit, attachment)
Parameters
limit: float
attachment: float
Returns
float

lev()

Limited expected value E[min(X, limit)].

Usage

lev(limit)
Parameters
limit: float
Returns
float

ln_pdf()

Log density at x.

Usage

ln_pdf(x)
Parameters
x: float
Returns
float

mean()

Mean of the distribution (inf if it does not exist).

Usage

mean()
Returns
float

quantile()

Quantile: the smallest x with P(X <= x) >= p.

Usage

quantile(p)
Parameters
p: float
Probability in [0, 1].
Returns
float
Raises
ValueError
If p is outside [0, 1].

sample()

n draws from stream stream of the generator keyed by

Usage

sample(n, seed, stream=0)

seed.

Parameters
n: int
seed: int
stream: int = 0
Returns
list of float

std()

Standard deviation of the distribution.

Usage

std()
Returns
float

stop_loss()

Expected excess over a retention, E[max(X - retention, 0)].

Usage

stop_loss(retention)
Parameters
retention: float
Returns
float

survival()

Survival function P(X > x), accurate far into the tail.

Usage

survival(x)
Parameters
x: float
Returns
float

variance()

Variance of the distribution (inf if it does not exist).

Usage

variance()
Returns
float