distributions.Tweedie
Tweedie distribution with mean mu, dispersion phi and power
Usage
distributions.Tweedie()1 < p < 2: variance phi * mu**p, a point mass at 0 and a continuous density above it.
It is a Poisson number of gamma losses, the GLM family for pure premium. P(Y = 0) = exp(-lambda_).
Parameters
mean: floatdispersion: floatpower: float-
In
(1, 2).
Raises
ValueError- If a parameter is out of range.
Examples
>>> import math
>>> from prospicio.distributions import Tweedie
>>> y = Tweedie(500.0, 40.0, 1.6)
>>> abs(y.cdf(0.0) - math.exp(-y.lambda_)) < 1e-15True
Attributes
| Name | Description |
|---|---|
| dispersion |
Dispersion phi.
|
| lambda_ | Poisson mean of the number of losses. |
| power | Power p. |
| severity | The gamma distribution of each loss. |
dispersion
Dispersion phi.
dispersion: float
lambda_
Poisson mean of the number of losses.
lambda_: float
power
Power p.
power: float
severity
The gamma distribution of each loss.
severity: Gamma
Methods
| Name | Description |
|---|---|
| cdf() |
Distribution function P(X <= x).
|
| from_poisson_gamma() | The Tweedie equal to a Poisson(lambda_) number of |
| 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 y > 0; at y = 0, the log of the point mass.
|
| 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_poisson_gamma()
The Tweedie equal to a Poisson(lambda_) number of
Usage
from_poisson_gamma(lambda_, shape, scale)Parameters
lambda_: floatshape: floatscale: float
Returns
Tweedie
layer()
Expected loss to the layer limit xs attachment.
Usage
layer(limit, attachment)Parameters
limit: float-
inffor 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)Parameters
limit: floatattachment: float
Returns
float
layer_variance()
Variance of the loss to the layer limit xs attachment.
Usage
layer_variance(limit, attachment)Parameters
limit: floatattachment: float
Returns
float
lev()
Limited expected value E[min(X, limit)].
Usage
lev(limit)Parameters
limit: float
Returns
float
ln_pdf()
Log density at y > 0; at y = 0, the log of the point mass.
Usage
ln_pdf(y)Parameters
y: 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: intseed: intstream: 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