Putting down some concepts and an implementation of certain probability distributions.

probdist.py

#Probability Distributions implemented interactively.
#An exercise in python mathematics and statistical methods
#I am developing this to further my understanding of bio-informatics by using
#a base-up approach.

import math
import random

class Binomial:
    '''The binomial distribution has two possible outcomes. which may be 
    thought of in terms of 1 or 0, True or False, Positive or Negative.
    Important parameters are the p value, which is the probability of yielding
    1 (the probability of getting 0 is then consequently (1 - p)) and N, the 
    number of tries.'''

    def __init__(self, N = 20, p = 0.5):
        if self.checkN(N):
            self.N = N
        else:
            self.N = 20
        if self.checkP(p):
            self.p = p
        else:
            self.p = 0.5

    def checkP(self, val):
        if 0 <= val <= 1:
            return True
        else:
            print('Invalid p value, must be between 0 and 1')
            return False

    def checkN(self, val):
        try:
            val = int(val)
            return True
        except ValueError:
            print('Invalid N value, must be an integer')
            return False

    def changeP(self, val):
        if self.checkP(val):
            self.p = val
        else:
            print('p value remains {0}'.format(self.p))

    def changeN(self, val):
        if self.checkN(val):
            self.N = val
        else:
            print('N value remains {0}'.format(self.N))

    def kProb(self, k, cumulative = '='):
        P = 0
        if 0 <= k <= self.N:
            if cumulative == '<':
                krange = xrange(0, k)
            elif cumulative == '>':
                krange = xrange(k +  1, self.N + 1)
            elif cumulative == '=':
                krange = [k]
            elif cumulative == '<=':
                krange = xrange(0, k + 1)
            elif cumulative == '>=':
                krange = xrange(k, self.N + 1)
            else:
                print('Improper control string: use \"<\", \">\", \"=\", \"<=\", or \">=\"')
                krange = False
            if krange:
                for kval in krange:
                    factnum = math.factorial(self.N)
                    factden = math.factorial(kval) * math.factorial(self.N - kval)
                    fact = factnum / factden
                    pek = self.p ** kval
                    ompenmk = (1.0 - self.p) ** (self.N - kval)
                    P += fact * pek * ompenmk
            return P

    def generateNull(self):
        nullstr = ''
        for each in xrange(self.N):
            r = random.random()
            if r > self.p:
                nullstr += '0'
            else:
                nullstr += '1'
        return nullstr

    def calculateVariance(self):
        pass

    def calculateMean(self):
        m = 0
        for kval in xrange(1, self.N + 1):
            m += kval * self.kProb(kval)
        return m

bn = Binomial()
#print(bn.generateNull())
#print(bn.calculateMean())
#print(bn.kProb(6, '='))
#print(bn.kProb(6, '<'))
#print(bn.kProb(6, '<='))
#print(bn.kProb(6, '>'))
#print(bn.kProb(6, '>='))