`numpy.random._generator:Generator.zipf`

Signature

def zipf ( a , size = None )

Summary

Draw samples from a Zipf distribution.

Extended Summary

Samples are drawn from a Zipf distribution with specified parameter a > 1.

The Zipf distribution (also known as the zeta distribution) is a discrete probability distribution that satisfies Zipf's law: the frequency of an item is inversely proportional to its rank in a frequency table.

Parameters

a : float or array_like of floats: Distribution parameter. Must be greater than 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 a is a scalar. Otherwise, np.array(a).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized Zipf distribution.

Notes

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

p (k) = \frac{k ^{- a}}{ζ ( a )},

for integers $k \geq 1$ , where $ζ$ is the Riemann Zeta function.

It is named for the American linguist George Kingsley Zipf, who noted that the frequency of any word in a sample of a language is inversely proportional to its rank in the frequency table.

Examples

Draw samples from the distribution:

a = 4.0
n = 20000
rng = np.random.default_rng()
s = rng.zipf(a, size=n)

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Display the histogram of the samples, along with the expected histogram based on the probability density function:

import matplotlib.pyplot as plt

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`bincount` provides a fast histogram for small integers.

count = np.bincount(s)
k = np.arange(1, s.max() + 1)

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plt.bar(k, count[1:], alpha=0.5, label='sample count')
plt.semilogy()

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plt.grid(alpha=0.4)

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plt.legend()
plt.title(f'Zipf sample, a={a}, size={n}')

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plt.show()

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Aliases

numpy.random.Generator.zipf