Source code for simplestatistics.statistics.binomial

from .choose import choose
from .decimalize import decimalize

def binom_single_calculation(k, n, p):
    # break the binomial distribution into three components
    # 1. n choose k
    component_1 = choose(n, k)

    # 2. p to the power k
    component_2 = pow(p, k)

    # 3. (1 - p) to the power (n - k)
    component_3 = pow((1 - p), (n - k))

    # return the product of the three components
    return(float(component_1 * component_2 * component_3))

[docs]def binomial(k, n, p): """ The `Binomial Distribution`_ is, quoting from the Wikipedia page: In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. .. _`binomial distribution`: https://en.wikipedia.org/wiki/Binomial_distribution Probability mass function equation: .. math:: f(k; n, p) = Pr(X = k) = \\binom{n}{k} p^k (1 - p)^{n-k} Args: k: Int or list of ints representing number of choices or successes. n: Int representing total number of trials. p: Float representing probability of success per trial. Returns: Float (or list of floats, if provided k was a list) representing probabilities of obtaining each k according to the binomial distribution. Examples: >>> binomial(4, 12, 0.2) 0.13287555072 >>> binomial([1, 2, 3], 10, 0.5) [0.009765625, 0.0439453125, 0.1171875] >>> binomial(4, 10, 1.5) Traceback (most recent call last): ... ValueError: probability cannot be greater than 1 or smaller than 0 """ # probability has to be between 0 and 1 if p > 1 or p < 0: raise ValueError('probability cannot be greater than 1 or smaller than 0') # decimalize probability to get # better precision p = decimalize(p) if type(k) in [int, float]: return(binom_single_calculation(k, n, p)) elif type(k) in [list, tuple]: binom_distribution_list = [binom_single_calculation(value, n, p) for value in k] return(binom_distribution_list)