Multivariate Distributions

Copulas library supports several Multivariate distributions that support working with multiple random variables at the same time, taking into account the dependcies that my exist between them.

• copulas.multivariate.GaussianMultivariate: Implements a multivariate distribution by combining the marginal univariate distributions with a Gaussian Copula.
• copulas.multivariate.VineCopula: Implements a multivariate distribution using Vine Copulas.

Gaussian Multivariate

from copulas.datasets import sample_trivariate_xyz
from copulas.visualization import scatter_3d

def func_Multivariate():
    data = sample_trivariate_xyz()
    print(data.head())
    scatter_3d(data)
    plt.show()

Fitting Model and Generating Synthetic Data by GaussianMultivariate class：

• Search for the Univariate distribution that better describes each column in the data.
• Fit the corresponding Univariate distributions to each column.
• Learn the joint distribution based on the correlations between the marginal distributions

def func_Multivariate():
    data = sample_trivariate_xyz()
    print(data.head())
    # scatter_3d(data)
    # plt.show()

    dist = GM()
    dist.fit(data)
    samples = dist.sample(1000)
    compare_3d(data, samples)

    plt.show()

Specifying column distributions. Advanced users can choose to manually specify the marginal distributions if they have additional information about the data.

dist = GaussianMultivariate(distribution=GaussianUnivariate)
dist.fit(data)
samples = dist.sample(1000)
compare_3d(data, samples)
plt.show()

By specifying the distribution that needs to be used in each column

dist = GaussianMultivariate(
        distribution = {
    
    
            'x': BetaUnivariate,
            'y': GaussianKDE,
            'z': GaussianUnivariate
        })
dist.fit(data)
samples = dist.sample(1000)
compare_3d(data, samples)
plt.show()

By specifying a family of Univariate

univ = Univariate(parametric=ParametricType.PARAMETRIC)
dist = GaussianMultivariate(distribution=univ)
dist.fit(data)
samples = dist.sample(1000)
compare_3d(data, samples)
plt.show()

Vine Copulas

The Vine Copulas work by building a vine over the different columns in the dataset and estimating the pairwise (bivariate) relationship between the nodes on every edge.

def func_VineCopulas():
    data = sample_trivariate_xyz()
    center = VineCopula('center') # C-Copula
    regular = VineCopula('regular') # R-Copula
    direct = VineCopula('direct') # D-Copula

    # Fitting data
    center.fit(data)
    regular.fit(data)
    direct.fit(data)

    c_samples = center.sample(1000)
    r_samples = regular.sample(1000)
    d_samples = direct.sample(1000)

    compare_3d(data, c_samples)
    plt.show()