Code example

To manually construct and visualize a simple mixed vine model:

from scipy.stats import norm, gamma, poisson
import numpy as np
from mixedvines.copula import Copula, GaussianCopula, ClaytonCopula, \
        FrankCopula
from mixedvines.mixedvine import MixedVine
import matplotlib.pyplot as plt
import itertools
# Manually construct mixed vine
dim = 3  # Dimension
vine = MixedVine(dim)
# Specify marginals
vine.set_marginal(0, norm(0, 1))
vine.set_marginal(1, poisson(5))
vine.set_marginal(2, gamma(2, 0, 4))
# Specify pair-copulas
vine.set_copula(1, 0, GaussianCopula(0.5))
vine.set_copula(1, 1, FrankCopula(4))
vine.set_copula(2, 0, ClaytonCopula(5))
# Calculate probability density function on lattice
bnds = np.empty((3), dtype=object)
bnds[0] = [-3, 3]
bnds[1] = [0, 15]
bnds[2] = [0.5, 25]
x0, x1, x2 = np.mgrid[bnds[0][0]:bnds[0][1]:0.05, bnds[1][0]:bnds[1][1],
                      bnds[2][0]:bnds[2][1]:0.1]
points = np.array([x0.ravel(), x1.ravel(), x2.ravel()]).T
pdf = vine.pdf(points)
pdf = np.reshape(pdf, x1.shape)
# Generate random variates
size = 100
samples = vine.rvs(size)
# Visualize 2d marginals and samples
comb = list(itertools.combinations(range(dim), 2))
for i, cmb in enumerate(comb):
    # Sum over all axes not in cmb
    cmb_inv = tuple(set(range(dim)) - set(cmb))
    margin = np.sum(pdf, axis=cmb_inv).T
    plt.subplot(2, len(comb), i + 1)
    plt.imshow(margin, aspect='auto', interpolation='none', cmap='hot',
               origin='lower', extent=[bnds[cmb[0]][0], bnds[cmb[0]][1],
                                       bnds[cmb[1]][0], bnds[cmb[1]][1]])
    plt.ylabel('$x_' + str(cmb[1]) + '$')
    plt.subplot(2, len(comb), len(comb) + i + 1)
    plt.scatter(samples[:, cmb[0]], samples[:, cmb[1]], s=1)
    plt.xlim(bnds[cmb[0]][0], bnds[cmb[0]][1])
    plt.ylim(bnds[cmb[1]][0], bnds[cmb[1]][1])
    plt.xlabel('$x_' + str(cmb[0]) + '$')
    plt.ylabel('$x_' + str(cmb[1]) + '$')
plt.tight_layout()
plt.show()

This code shows the 2d marginals and 100 samples of a 3d mixed vine.