Mathematical computation and visualization of bivariate copulas.
Project description
copulas_in_systemic_risk
Copula properties
For any of the copula families below, e.g. copula = copul.Galambos()
, get the following properties:
- Cumulative distribution function via copula.cdf
- Density function via copula.pdf
Supported copula families:
Archimedean Copulas
The 22 copula families from Nelsen, accessible via
copul.archimedean.Nelsen1
, copul.archimedean.Nelsen2
, etc.
Let copula
be any instance of those classes, e.g. copula = copul.archimedean.Nelsen1()
.
For these families, the following properties are available:
- generator function is available via e.g.
copula.generator
- inverse generator function is available via e.g.
copula.inverse_generator
- CI char function is available via e.g.
copula.ci_char
- the MTP2 char function is available via e.g.
copula.mtp2_char
Extreme Value Copulas
- BB5
- Cuadras-Augé
- Galambos
- Gumbel
- Husler-Reiss
- Joe
- Marshall-Olkin
- tEV
- tawn
Let copula
be any instance of those classes, e.g. copula = copul.extreme_value.Galambos()
.
Then, the Pickand function is available via e.g. copula.pickand
.
Other
- Farlie-Gumbel-Morgenstern
- Fréchet
- Mardia
- Plackett
- Raftery
Sample Usage
import copul
galambos = copul.extreme_value.Galambos()
params = galambos.sample_parameters(3)
galambos.plot_pickand(params)
clayton = copul.archimedean.Clayton()
clayton(theta=1.5).plot_cdf()
clayton(theta=2.5).plot_pdf()
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