maxframe.tensor.random.zipf#

maxframe.tensor.random.zipf(a, size=None, chunk_size=None, gpu=None, dtype=None)[source]#

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), then m * n * k samples are drawn. If size is None (default), a single value is returned if a is a scalar. Otherwise, mt.array(a).size samples are drawn.

  • chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension

  • gpu (bool, optional) – Allocate the tensor on GPU if True, False as default

  • dtype (data-type, optional) – Data-type of the returned tensor.

Returns:

out – Drawn samples from the parameterized Zipf distribution.

Return type:

Tensor or scalar

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

Examples

Draw samples from the distribution:

>>> import maxframe.tensor as mt

>>> a = 2. # parameter
>>> s = mt.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].execute(), 50, normed=True)
>>> x = mt.arange(1., 50.)
>>> y = x**(-a) / special.zetac(a)
>>> plt.plot(x.execute(), (y/mt.max(y)).execute(), linewidth=2, color='r')
>>> plt.show()
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