numpy.random.zipf
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random.zipf(a, size=None)
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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.
Note
New code should use the
zipf
method of adefault_rng()
instance instead; please see the Quick Start.- Parameters
-
-
afloat or array_like of floats
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Distribution parameter. Must be greater than 1.
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sizeint or tuple of ints, optional
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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
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outndarray or scalar
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Drawn samples from the parameterized Zipf distribution.
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See also
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scipy.stats.zipf
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probability density function, distribution, or cumulative density function, etc.
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Generator.zipf
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which should be used for new code.
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
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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()
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https://numpy.org/doc/1.21/reference/random/generated/numpy.random.zipf.html