`scipy.stats._discrete_distns:zipfian_gen`

source: /scipy/stats/_discrete_distns.py :1370

Signature

   class     zipfian_gen (    a    =  0   ,    b    =  inf   ,    name    =  None   ,    badvalue    =  None   ,    moment_tol    =  1e-08   ,    values    =  None   ,    inc    =  1   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

A Zipfian discrete random variable.

Extended Summary

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Notes

The probability mass function for zipfian is:

f (k, a, n) = \frac{1}{H _{n, a} k ^{a}}

for $k \in {1, 2, \dots, n - 1, n}$ , $a \geq 0$ , $n \in {1, 2, 3, \dots}$ .

zipfian takes $a$ and $n$ as shape parameters. $H_{n, a}$ is the $n$ th generalized harmonic number of order $a$ .

The SciPy implementation of this distribution requires $1 \leq n \leq 2^{53}$ . For larger values of $n$ , the zipfian methods (pmf, cdf, mean, etc.) will return nan.

When $a > 1$ , the Zipfian distribution reduces to the Zipf (zeta) distribution as $n \to \infty$ .

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Aliases

scipy.stats._discrete_distns.zipfian_gen