numpy.random.zipf¶

numpy.random.zipf(a, size=None)¶

Draw samples from a Zipf distribution.

Samples are drawn from a Zipf distribution with specified parameter (a), where a > 1.

The zipf distribution (also known as the zeta distribution) is a continuous probability distribution that satisfies Zipf’s law, where the frequency of an item is inversely proportional to its rank in a frequency table.

Parameters:

a : float

parameter, > 1.

size : {tuple, int}

Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn.

Returns:

samples : {ndarray, scalar}

The returned samples are greater than or equal to one.

See also

scipy.stats.distributions.zipf: probability density function, distribution or cumulative density function, etc.

Notes

The probability density for the Zipf distribution is

$p(x) = \frac{x^{-a}}{\zeta(a)},$

where $\zeta$ is the Riemann Zeta function.

Named after 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.

References

[R263]

Weisstein, Eric W. “Zipf Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/ZipfDistribution.html

[R264]

Wikipedia, “Zeta distribution”, http://en.wikipedia.org/wiki/Zeta_distribution

[R265]

Wikipedia, “Zipf’s Law”, http://en.wikipedia.org/wiki/Zipf%27s_law

[R266]

Zipf, George Kingsley (1932): Selected Studies of the Principle of Relative Frequency in Language. Cambridge (Mass.).

Examples