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A python library for building different types of copulas and using them for sampling.

Project description

“sdv-dev” An open source project from Data to AI Lab at MIT.

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Copulas is a Python library for modeling multivariate distributions and sampling from them using copula functions. Given a table containing numerical data, we can use Copulas to learn the distribution and later on generate new synthetic rows following the same statistical properties.

Some of the features provided by this library include:

  • A variety of distributions for modeling univariate data.
  • Multiple Archimedean copulas for modeling bivariate data.
  • Gaussian and Vine copulas for modeling multivariate data.
  • Automatic selection of univariate distributions and bivariate copulas.

Supported Distributions


  • Gaussian
  • Student T
  • Beta
  • Gamma
  • Gaussian KDE
  • Truncated Gaussian

Archimedean Copulas (Bivariate)

  • Clayton
  • Frank
  • Gumbel


  • Gaussian
  • D-Vine
  • C-Vine
  • R-Vine



Copulas has been developed and tested on Python 3.5, 3.6 and 3.7

Also, although it is not strictly required, the usage of a virtualenv is highly recommended in order to avoid interfering with other software installed in the system where Copulas is run.

Install with pip

The easiest and recommended way to install Copulas is using pip:

pip install copulas

This will pull and install the latest stable release from PyPi.

If you want to install from source or contribute to the project please read the Contributing Guide.


In this short quickstart, we show how to model a multivariate dataset and then generate synthetic data that resembles it.

import warnings

from copulas.datasets import sample_trivariate_xyz
from copulas.multivariate import GaussianMultivariate
from copulas.visualization import compare_3d

# Load a dataset with 3 columns that are not independent
real_data = sample_trivariate_xyz()

# Fit a gaussian copula to the data
copula = GaussianMultivariate()

# Sample synthetic data
synthetic_data = copula.sample(len(real_data))

# Plot the real and the synthetic data to compare
compare_3d(real_data, synthetic_data)

The output will be a figure with two plots, showing what both the real and the synthetic data that you just generated look like:


What's next?

For more details about Copulas and all its possibilities and features, please check the documentation site.

There you can learn more about how to contribute to Copulas in order to help us developing new features or cool ideas.


Copulas is an open source project from the Data to AI Lab at MIT which has been built and maintained over the years by the following team:

Related Projects


SDV, for Synthetic Data Vault, is the end-user library for synthesizing data in development under the HDI Project. SDV allows you to easily model and sample relational datasets using Copulas thought a simple API. Other features include anonymization of Personal Identifiable Information (PII) and preserving relational integrity on sampled records.


CTGAN is a GAN based model for synthesizing tabular data. It's also developed by the MIT's Data to AI Lab and is under active development.


0.3.3 (2020-09-18)

General Improvements

Use corr instead of cov in the GaussianMultivariate - Issue #195 by @rollervan Add arguments to GaussianKDE - Issue #181 by @rollervan

New Features

Log Laplace Distribution - Issue #188 by @rollervan

0.3.2 (2020-08-08)

General Improvements

  • Support Python 3.8 - Issue #185 by @csala
  • Support scipy <1.3 - Issue #180 by @csala

New Features

  • Add Uniform Univariate - Issue #179 by @rollervan

0.3.1 (2020-07-09)

General Improvements

  • Raise numpy version upper bound to 2 - Issue #178 by @csala

New Features

  • Add Student T Univariate - Issue #172 by @gbonomib

Bug Fixes

  • Error in Quickstarts : Unknown projection '3d' - Issue #174 by @csala

0.3.0 (2020-03-27)

Important revamp of the internal implementation of the project, the testing infrastructure and the documentation by Kevin Alex Zhang @k15z, Carles Sala @csala and Kalyan Veeramachaneni @kveerama


  • Reimplementation of the existing Univariate distributions.
  • Addition of new Beta and Gamma Univariates.
  • New Univariate API with automatic selection of the optimal distribution.
  • Several improvements and fixes on the Bivariate and Multivariate Copulas implementation.
  • New visualization module with simple plotting patterns to visualize probability distributions.
  • New datasets module with toy datasets sampling functions.
  • New testing infrastructure with end-to-end, numerical and large scale testing.
  • Improved tutorials and documentation.

0.2.5 (2020-01-17)

General Improvements

  • Convert import_object to get_instance - Issue #114 by @JDTheRipperPC

0.2.4 (2019-12-23)

New Features

  • Allow creating copula classes directly - Issue #117 by @csala

General Improvements

  • Remove select_copula from Bivariate - Issue #118 by @csala

  • Rename TruncNorm to TruncGaussian and make it non standard - Issue #102 by @csala @JDTheRipperPC

Bugs fixed

  • Error on Frank and Gumble sampling - Issue #112 by @csala

0.2.3 (2019-09-17)

New Features

  • Add support to Python 3.7 - Issue #53 by @JDTheRipperPC

General Improvements

  • Document RELEASE workflow - Issue #105 by @JDTheRipperPC

  • Improve serialization of univariate distributions - Issue #99 by @ManuelAlvarezC and @JDTheRipperPC

Bugs fixed

  • The method 'select_copula' of Bivariate return wrong CopulaType - Issue #101 by @JDTheRipperPC

0.2.2 (2019-07-31)

New Features

  • truncnorm distribution and a generic wrapper for scipy.rv_continous distributions - Issue #27 by @amontanez, @csala and @ManuelAlvarezC
  • Independence bivariate copulas - Issue #46 by @aliciasun, @csala and @ManuelAlvarezC
  • Option to select seed on random number generator - Issue #63 by @echo66 and @ManuelAlvarezC
  • Option on Vine copulas to select number of rows to sample - Issue #77 by @ManuelAlvarezC
  • Make copulas accept both scalars and arrays as arguments - Issues #85 and #90 by @ManuelAlvarezC

General Improvements

  • Ability to properly handle constant data - Issues #57 and #82 by @csala and @ManuelAlvarezC
  • Tests for analytics properties of copulas - Issue #61 by @ManuelAlvarezC
  • Improved documentation - Issue #96 by @ManuelAlvarezC

Bugs fixed

  • Fix bug on Vine copulas, that made it crash during the bivariate copula selection - Issue #64 by @echo66 and @ManuelAlvarezC

0.2.1 - Vine serialization

  • Add serialization to Vine copulas.
  • Add distribution as argument for the Gaussian Copula.
  • Improve Bivariate Copulas code structure to remove code duplication.
  • Fix bug in Vine Copulas sampling: 'Edge' object has no attribute 'index'
  • Improve code documentation.
  • Improve code style and linting tools configuration.

0.2.0 - Unified API

  • New API for stats methods.
  • Standarize input and output to numpy.ndarray.
  • Increase unittest coverage to 90%.
  • Add methods to load/save copulas.
  • Improve Gaussian copula sampling accuracy.

0.1.1 - Minor Improvements

  • Different Copula types separated in subclasses
  • Extensive Unit Testing
  • More pythonic names in the public API.
  • Stop using third party elements that will be deprected soon.
  • Add methods to sample new data on bivariate copulas.
  • New KDE Univariate copula
  • Improved examples with additional demo data.

0.1.0 - First Release

  • First release on PyPI.

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