CODEWITHSUNDEEP
pythonrandomprobabilitycoin-flipping
Pratik Deoghare
Pratik Deoghare

Reputation: 37172

How do I simulate flip of biased coin?

In unbiased coin flip H or T occurs 50% of times.

But I want to simulate coin which gives H with probability 'p' and T with probability '(1-p)'.

something like this:

def flip(p):
   '''this function return H with probability p'''
   # do something
   return result

>> [flip(0.8) for i in xrange(10)]
[H,H,T,H,H,H,T,H,H,H]

Upvotes: 37

Views: 55448

Answers (7)

Rumi
Rumi

Reputation: 196

import random
def flip():
    return ["H" if random.randint(0,3) <= 2 else "T" for i in range(10)]

Right now probability of Head is 75% and tails is 25% (0,1,2 are all Heads and only 3 is Tails) . By using random.randint() you could have any probability of bias while still maintaining randomness.

Upvotes: 0

Sandipan Dey
Sandipan Dey

Reputation: 23101

One can sample from the X ~ Bernoulli(p) distribution nsamples times using sympy too:

from sympy.stats import Bernoulli, sample_iter
list(sample_iter(Bernoulli('X', 0.8), numsamples=10)) # p = 0.8 and nsamples=10
# [1, 1, 0, 1, 1, 0, 1, 1, 1, 1]

Return 'H' or 'T' instead using

def flip(p, n):
    return list(map(lambda x: 'H' if x==1 else 'T', sample_iter(Bernoulli('X', p), numsamples=n)))

print(flip(0.8, 10)) # p = 0.8 and nsamples=10
# ['H', 'H', 'T', 'H', 'H', 'T', 'H', 'H', 'H', 'H']

Upvotes: 2

ticktock
ticktock

Reputation: 637

How about:

import numpy as np
n, p = 1, .33  # n = coins flipped, p = prob of success
s = np.random.binomial(n, p, 100)

Upvotes: 6

nosklo
nosklo

Reputation: 222802

Do you want the "bias" to be based in symmetric distribuition? Or maybe exponential distribution? Gaussian anyone?

Well, here are all the methods, extracted from random documentation itself.

First, an example of triangular distribution:

print random.triangular(0, 1, 0.7)

random.triangular(low, high, mode):

Return a random floating point number N such that low <= N < high and with the specified mode between those bounds. The low and high bounds default to zero and one. The mode argument defaults to the midpoint between the bounds, giving a symmetric distribution.

random.betavariate(alpha, beta):

Beta distribution. Conditions on the parameters are alpha > 0 and beta > 0. Returned values range between 0 and 1.

random.expovariate(lambd):

Exponential distribution. lambd is 1.0 divided by the desired mean. It should be nonzero. (The parameter would be called “lambda”, but that is a reserved word in Python.) Returned values range from 0 to positive infinity if lambd is positive, and from negative infinity to 0 if lambd is negative.

random.gammavariate(alpha, beta):

Gamma distribution. (Not the gamma function!) Conditions on the parameters are alpha > 0 and beta > 0.

random.gauss(mu, sigma):

Gaussian distribution. mu is the mean, and sigma is the standard deviation. This is slightly faster than the normalvariate() function defined below.

random.lognormvariate(mu, sigma):

Log normal distribution. If you take the natural logarithm of this distribution, you’ll get a normal distribution with mean mu and standard deviation sigma. mu can have any value, and sigma must be greater than zero.

random.normalvariate(mu, sigma):

Normal distribution. mu is the mean, and sigma is the standard deviation.

random.vonmisesvariate(mu, kappa):

mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa is the concentration parameter, which must be greater than or equal to zero. If kappa is equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2*pi.

random.paretovariate(alpha):

Pareto distribution. alpha is the shape parameter.

random.weibullvariate(alpha, beta)

Weibull distribution. alpha is the scale parameter and beta is the shape parameter.

Upvotes: 11

Federico A. Ramponi
Federico A. Ramponi

Reputation: 47075

random.random() returns a uniformly distributed pseudo-random floating point number in the range [0, 1). This number is less than a given number p in the range [0,1) with probability p. Thus:

def flip(p):
    return 'H' if random.random() < p else 'T'

Some experiments:

>>> N = 100
>>> flips = [flip(0.2) for i in xrange(N)]
>>> float(flips.count('H'))/N
0.17999999999999999  # Approximately 20% of the coins are heads

>>> N = 10000
>>> flips = [flip(0.2) for i in xrange(N)]
>>> float(flips.count('H'))/N
0.20549999999999999  # Better approximation

Upvotes: 59

Paul
Paul

Reputation: 6439

  • Import a random number between 0 - 1 (you can use randrange function)

  • If the number is above (1-p), return tails.

  • Else, return heads

Upvotes: 0

David Z
David Z

Reputation: 131550

import random
def flip(p):
    return (random.random() < p)

That returns a boolean which you can then use to choose H or T (or choose between any two values) you want. You could also include the choice in the method:

def flip(p):
    if random.random() < p:
        return 'H'
    else:
        return 'T'

but it'd be less generally useful that way.

Upvotes: 5

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