numpy.random.RandomState.zipf¶
-
RandomState.
zipf
(a, size=None)¶ 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.
Parameters: - a : float or array_like of floats
Distribution parameter. Should be greater than 1.
- size : int or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifa
is a scalar. Otherwise,np.array(a).size
samples are drawn.
Returns: - out : ndarray or scalar
Drawn samples from the parameterized Zipf distribution.
See also
scipy.stats.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.
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.
References
[1] Zipf, G. K., “Selected Studies of the Principle of Relative Frequency in Language,” Cambridge, MA: Harvard Univ. Press, 1932. Examples
Draw samples from the distribution:
>>> a = 2. # parameter >>> s = np.random.zipf(a, 1000)
Display the histogram of the samples, along with the probability density function:
>>> import matplotlib.pyplot as plt >>> from scipy import special
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) >>> plt.plot(x, y/max(y), linewidth=2, color='r') >>> plt.show()