zipf distribution¶

group turbo_random_zipf

Functions

template<typename IntType, typename URBG> IntType zipf(URBG &&urbg, IntType hi = (std::numeric_limits<IntType>::max)(), double q = 2.0, double v = 1.0)¶

turbo::zipf<T>(bitgen, hi = max, q = 2, v = 1) turbo::zipf produces discrete probabilities commonly used for modelling of rare events over the closed interval [0, hi].

The parameters v and q determine the skew of the distribution. T must be an integral type, but may be inferred from the type of hi.

See http://mathworld.wolfram.com/ZipfDistribution.html

Example:

turbo::BitGen bitgen;
...
int term_rank = turbo::zipf<int>(bitgen);

Template Parameters:

IntType –
URBG –

Parameters:

urbg –
hi –
q – = 2 default
v –

Returns:

IntType

template<typename IntType = int> class zipf_distribution¶

#include <zipf_distribution.h>

turbo::zipf_distribution produces random integer-values in the range [0, k], distributed according to the unnormalized discrete probability function:

P(x) = (v + x) ^ -q

The parameter v must be greater than 0 and the parameter q must be greater than 1. If either of these parameters take invalid values then the behavior is undefined.

IntType is the result_type generated by the generator. It must be of integral type; a static_assert ensures this is the case.

The implementation is based on W.Hormann, G.Derflinger:

“Rejection-Inversion to Generate Variates from Monotone Discrete

Distributions”

http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz