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networkx.utils.random_sequence.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

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

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

Parameters:
  • alpha (float) – Exponent value of the distribution
  • xmin (int) – Minimum value
  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.
Returns:

x – Random value from Zipf distribution
Return type:

int
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.

Examples

>>> nx.zipf_rv(alpha=2, xmin=3, seed=42)  # doctest: +SKIP

References

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