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
size : {tuple, int}
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Returns : | samples : {ndarray, scalar}
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See also
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
[R220] | Weisstein, Eric W. “Zipf Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/ZipfDistribution.html |
[R221] | Wikipedia, “Zeta distribution”, http://en.wikipedia.org/wiki/Zeta_distribution |
[R222] | Wikipedia, “Zipf’s Law”, http://en.wikipedia.org/wiki/Zipf%27s_law |
[R223] | Zipf, George Kingsley (1932): Selected Studies of the Principle of Relative Frequency in Language. Cambridge (Mass.). |
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
>>> import scipy.special as sps
Truncate s values at 50 so plot is interesting
>>> count, bins, ignored = plt.hist(s[s<50], 50, normed=True)
>>> x = np.arange(1., 50.)
>>> y = x**(-a)/sps.zetac(a)
>>> plt.plot(x, y/max(y), linewidth=2, color='r')
>>> plt.show()