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pycopula

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Python copulas library for dependency modeling

// repository documentation

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![Screenshot](https://raw.githubusercontent.com/MaximeJumelle/pycopula/master/resources/logo.png)

PyCopula is an easy-to-use Python library that allows you to study random variables dependencies with copulas. It comes with useful tools and features to plot, estimate or simulate on copulas.

* [Online Documentation](https://blent-ai.github.io/pycopula)

## Installation
Installation via *pip* always offers you the last stable version of the package.
```
pip install pycopula
```
However, if you are looking for latest updates, consider installation directly from sources.
```
git clone https://github.com/MaximeJumelle/pycopula.git
cd pycopula
python setup.py install
```

## Features
PyCopula natively handle various families of copulas including :
- Archimean Copulas
	- Clayton
	- Gumbel
	- Joe
	- Frank
	- Ali-Mikhail-Haq
- Elliptic Copulas
	- Gaussian
	- Student

### Estimation
Three methods of estimation, based on *SciPy* numerical optimization routines, are available to provide high flexibility during fitting process.
- Moments estimation on particular copulas
- Maximum Likelihood Estimation (MLE)
- Inference For Margins (IFM)
- Canonical Maximum Likelihood Estimation (CMLE)

## Usage
PyCopula was designed to provide an easy-to-use interface that does not require a lot in both programming and computing. As a result, only a few lines are needed to properly fit any copulas, as demonstrated in the following code snippet.
```python
import pandas as pd
from pycopula.copula import ArchimedeanCopula

data = pd.read_csv("data/classic.csv").values[:,1:]

archimedean = ArchimedeanCopula(family="gumbel", dim=2)
archimedean.fit(data, method="cmle")
```
```console
Archimedean Copula (gumbel) :
*	Parameter : 1.605037
```

## Visualization

#### 3D PDF and CDF

![Screenshot](https://github.com/MaximeJumelle/pycopula/blob/master/resources/gaussian_pdf_cdf.png?raw=true)

#### Concentration Functions

![Screenshot](https://raw.githubusercontent.com/MaximeJumelle/pycopula/master/resources/lower_upper_tail.png)

#### Estimation

#### Simulation

![Screenshot](https://raw.githubusercontent.com/MaximeJumelle/pycopula/master/resources/simulation_gaussian.png)

## Development

Currently, there are only a few features implemented in the library, which are the basics components for copula handling :

- Creating Archimedean, Gaussian and Student copulas
- 3D plot of PDF and CDF
- Concentration functions and visualization
- Estimation of copulas parameters (CMLE, MLE, IFM)

In the future, I plan to release the following features :

- Goodness-of-fit
- Copula selection with criterions and statistical testing
- Examples of applications in real world with open data

Also, if you are interested in the project, I would be happy to collaborate with you since there are still quite a lot of improvements needed (computation, estimation methods, visualization) and that I don't have enough time on my hands to do it quickly.

pycopula

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