zipf_rv¶

zipf_rv(alpha, xmin=1, seed=None)[source]¶

Return a random value chosen from the Zipf distribution.

The return value is an integer drawn from the probability distribution ::math:

p(x)=\frac{x^{-\alpha}}{\zeta(\alpha,x_{min})},

where \(\zeta(\alpha,x_{min})\) is the Hurwitz zeta function.

Parameters :

alpha : float

Exponent value of the distribution

xmin : int

Minimum value

seed : int

Seed value for random number generator

Returns :

x : int

Random value from Zipf distribution

Raises :

ValueError:

If xmin < 1 or If alpha <= 1

Notes

The rejection algorithm generates random values for a the power-law distribution in uniformly bounded expected time dependent on parameters. See [1] for details on its operation.

References

..[1] Luc Devroye, Non-Uniform Random Variate Generation,: Springer-Verlag, New York, 1986.

Examples

>>> nx.zipf_rv(alpha=2, xmin=3, seed=42) 