Draw samples from a Zipf distribution.
Samples are drawn from a Zipf distribution with specified parameter a > 1.
The Zipf distribution (also known as the zeta distribution) is a continuous probability distribution that satisfies Zipf’s law: the frequency of an item is inversely proportional to its rank in a frequency table.
- 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 * ksamples are drawn. If size is
None(default), a single value is returned if
ais a scalar. Otherwise,
np.array(a).sizesamples are drawn.
- out : ndarray or scalar
Drawn samples from the parameterized Zipf distribution.
- probability density function, distribution, or cumulative density function, etc.
The probability density for the Zipf distribution is
where 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.
 Zipf, G. K., “Selected Studies of the Principle of Relative Frequency in Language,” Cambridge, MA: Harvard Univ. Press, 1932.
Draw samples from the distribution:
>>> a = 2. # parameter >>> s = np.random.default_rng().zipf(a, 1000)
Display the histogram of the samples, along with the probability density function:
>>> import matplotlib.pyplot as plt >>> from scipy import special # doctest: +SKIP
Truncate s values at 50 so plot is interesting:
>>> count, bins, ignored = plt.hist(s[s<50], ... 50, density=True) >>> x = np.arange(1., 50.) >>> y = x**(-a) / special.zetac(a) # doctest: +SKIP >>> plt.plot(x, y/max(y), linewidth=2, color='r') # doctest: +SKIP >>> plt.show()