copula.py

# source: http://firsttimeprogrammer.blogspot.com/2015/02/copulalib-how-to-use-copulas-in-python.html

import numpy as np
import matplotlib.pyplot as plt
from copulalib.copulalib import Copula
plt.style.use('ggplot')

def generateData():
    global x,y
    x = np.random.normal(size=250)
    y = 2.5*x + np.random.normal(size=250)

# Data and histograms
def plotData():
    global x,y
    fig = plt.figure()
    fig.add_subplot(2,2,1)
    plt.hist(x,bins=20,color='green',alpha=0.8,align='mid')
    plt.title('X variable distribution')
    fig.add_subplot(2,2,3)
    plt.scatter(x,y,marker="o",alpha=0.8)
    fig.add_subplot(2,2,4)
    plt.title('Joint X,Y')
    plt.hist(y,bins=20,orientation='horizontal',color='red',alpha=0.8,align='mid')
    plt.title('Y variable distribution')    
    plt.show()

def generateCopulas():
    global x,y
    fig = plt.figure()

    frank = Copula(x,y,family='frank')
    uf,vf = frank.generate_uv(1000)
    fig.add_subplot(2,2,1)
    plt.scatter(uf,vf,marker='.',color='blue')
    plt.ylim(0,1)
    plt.xlim(0,1)
    plt.title('Frank copula')

    clayton = Copula(x,y,family='clayton')
    uc,vc = clayton.generate_uv(1000)
    fig.add_subplot(2,2,2)
    plt.scatter(uc,vc,marker='.',color='red')
    plt.ylim(0,1)
    plt.xlim(0,1)
    plt.title('Clayton copula')

    gumbel = Copula(x,y,family='gumbel')
    ug,vg = gumbel.generate_uv(1000)
    fig.add_subplot(2,2,3)
    plt.scatter(ug,vg,marker='.',color='green')
    plt.ylim(0,1)
    plt.xlim(0,1)
    plt.title('Gumbel copula')

    plt.show()

#---
# Run the functions

generateData()
plotData()
generateCopulas()