zipf(self, a, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.zipf.
Some inconsistencies with the Dask version may exist.
Samples are drawn from a Zipf distribution with specified parameter a > 1.
The Zipf distribution (also known as the zeta distribution) is a discrete probability distribution that satisfies Zipf's law: the frequency of an item is inversely proportional to its rank in a frequency table.
New code should use the zipf
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
The probability density for the Zipf distribution is
$$p(k) = \frac{k^{-a}}{\zeta(a)},$$for integers $k \geq 1$ , 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.
Distribution parameter. Must be greater than 1.
Output shape. If the given shape is, e.g., (m, n, k)
, then m * n * k
samples are drawn. If size is None
(default), a single value is returned if a
is a scalar. Otherwise, np.array(a).size
samples are drawn.
Drawn samples from the parameterized Zipf distribution.
Draw samples from a Zipf distribution.
Generator.zipf
which should be used for new code.
scipy.stats.zipf
probability density function, distribution, or cumulative density function, etc.
Draw samples from the distribution:
This example is valid syntax, but we were not able to check execution>>> a = 4.0 # doctest: +SKIP
... n = 20000 # doctest: +SKIP
... s = np.random.zipf(a, n) # doctest: +SKIP
Display the histogram of the samples, along with the expected histogram based on the probability density function:
This example is valid syntax, but we were not able to check execution>>> import matplotlib.pyplot as plt # doctest: +SKIP
... from scipy.special import zeta # doctest: +SKIP
bincount
provides a fast histogram for small integers.
>>> count = np.bincount(s) # doctest: +SKIPThis example is valid syntax, but we were not able to check execution
... k = np.arange(1, s.max() + 1) # doctest: +SKIP
>>> plt.bar(k, count[1:], alpha=0.5, label='sample count') # doctest: +SKIPSee :
... plt.plot(k, n*(k**-a)/zeta(a), 'k.-', alpha=0.5, # doctest: +SKIP
... label='expected count') # doctest: +SKIP
... plt.semilogy() # doctest: +SKIP
... plt.grid(alpha=0.4) # doctest: +SKIP
... plt.legend() # doctest: +SKIP
... plt.title(f'Zipf sample, a={a}, size={n}') # doctest: +SKIP
... plt.show() # doctest: +SKIP
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them