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bundles / numpy 2.4.4 / numpy / random / _generator / Generator / binomial

cython_function_or_method

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

where is the number of trials, is the probability of success, and 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')
✗

See also

scipy.stats.binom

probability density function, distribution or cumulative density function, etc.

Aliases

  • numpy.random.Generator.binomial

Referenced by

This package