Probability Distribution

distribution.py

#!/usr/bin/python

import pylab
import random
import math

def uniform():
    result = {}
    hist = []
    a = 100
    b = 200
    for i in xrange(100000):
        u =random.random()
        rv = round(a + (b - a) * u, 0)
        hist.append(rv)
        if result.has_key(rv):
            result[rv] += 1
        else:
            result[rv] = 1

    pylab.plot(result.keys(), result.values(), '.')
    pylab.xlabel("Random Variables")
    pylab.ylabel("Number of occurences")
    pylab.title("Uniform Probability distribution")
    pylab.grid(True)
    pylab.savefig("uniform_gra.png")
    # pylab.show()
    pylab.cla()

    pylab.hist(hist, bins=100)
    pylab.xlabel("Random Vars")
    pylab.ylabel("freq")
    pylab.title("uniform dist")
    pylab.grid(True)
    pylab.savefig("uniform_hist.png")
    # pylab.show()
    pylab.cla()

    print "uniform distribution mean: ", sum(hist)/len(hist)

def exponential():
    result = {}
    hist = []
    m = 150
    for i in xrange(100000):
        u =random.random()
        # rv = round(a + (b - a) * u, 0)
        rv = round(-m * math.log(u), 0)
        hist.append(rv)
        if result.has_key(rv):
            result[rv] += 1
        else:
            result[rv] = 1

    pylab.plot(result.keys(), result.values(), '.')
    pylab.xlabel("Random Variables")
    pylab.ylabel("Number of occurences")
    pylab.title("Exponential Probability distribution")
    pylab.grid(True)
    pylab.savefig("exp_gra.png")
    # pylab.show()
    pylab.cla()

    pylab.hist(hist, bins=100)
    pylab.xlabel("Random Vars")
    pylab.ylabel("freq")
    pylab.title("Exponential dist")
    pylab.grid(True)
    pylab.savefig("exp_hist.png")
    # pylab.show()
    pylab.cla()

def main():
    uniform()
    exponential()

if __name__ == "__main__":
    main()