`numpy.random._generator:Generator.binomial`

Signature

def binomial ( n , p , size = None )

Summary

Draw samples from a binomial distribution.

Extended Summary

Samples are drawn from a binomial distribution with specified parameters, n trials and p probability of success where n an integer >= 0 and p is in the interval [0,1]. (n may be input as a float, but it is truncated to an integer in use)

Parameters

n : int or array_like of ints: Parameter of the distribution, >= 0. Floats are also accepted, but they will be truncated to integers.
p : float or array_like of floats: Parameter of the distribution, >= 0 and <=1.
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if n and p are both scalars. Otherwise, np.broadcast(n, p).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized binomial distribution, where each sample is equal to the number of successes over the n trials.

Notes

The probability mass function (PMF) for the binomial distribution is

P (N) = (N n) p^{N} (1 - p)^{n - N},

where $n$ is the number of trials, $p$ is the probability of success, and $N$ is the number of successes.

When estimating the standard error of a proportion in a population by using a random sample, the normal distribution works well unless the product p*n <=5, where p = population proportion estimate, and n = number of samples, in which case the binomial distribution is used instead. For example, a sample of 15 people shows 4 who are left handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4, so the binomial distribution should be used in this case.

Examples

Draw samples from the distribution:

rng = np.random.default_rng()
n, p, size = 10, .5, 10000
s = rng.binomial(n, p, 10000)

✓

Assume a company drills 9 wild-cat oil exploration wells, each with an estimated probability of success of ``p=0.1``. All nine wells fail. What is the probability of that happening? Over ``size = 20,000`` trials the probability of this happening is on average:

n, p, size = 9, 0.1, 20000

✓

np.sum(rng.binomial(n=n, p=p, size=size) == 0)/size

✗

The following can be used to visualize a sample with ``n=100``, ``p=0.4`` and the corresponding probability density function:

import matplotlib.pyplot as plt
from scipy.stats import binom
n, p, size = 100, 0.4, 10000
sample = rng.binomial(n, p, size=size)
count, bins, _ = plt.hist(sample, 30, density=True)
x = np.arange(n)
y = binom.pmf(x, n, p)

✓

plt.plot(x, y, linewidth=2, color='r')

`numpy.random._generator:Generator.binomial`

Signature

Summary

Extended Summary

Parameters

Returns

Notes

Examples

See also

Aliases

Referenced by

This package