###A C++ library for generating discrete random numbers according to the Zipf-Mandelbrot distrbution.
The Zipf-Mandelbrot distribution finds uses in many applications. The general form of the probability mass function is:
f(k;N,q,s) = 1/( H(N,q,s)*(k+q)^s )
where
H(N,q,s) = sum_(n=1)^(N) 1/(n+q)^s
and,
s,N > 1 and q >= 0
When q = 0 this becomes the mass function for Zipf's Law
When N -> infinity this becomes the Hurwitz Zeta mass function
When N -> infinity and q = 0, this becomes the Riemann Zeta mass function
The approach taken here is to generate a table of probabilities according to the paramaters N, q and s, and then use a general purpose algorithm for generating discrete random numbers.
All classes are designed to work within the C++11 standard framework for Pseudo-random number generation.
rng::zipf_mandelbrot_distribution: A template class for creating the random numbers. It takes as input, the values for N, q and s, and, as template parameter, a class for creating discrete random numbers. Although this class can work with, std::discrete_distribution, from C++11, we provide two other templates that are more efficient.
rng::discrete_distribution: A class using Walker's histogram algorithm to generate discrete random numbers. The tables are created using Vose's algorithm.
rng::discrete_distribution_30bit: This class uses the MTW (Marsaglia, Tsang and Wang) algorithm for creating the discrete random numbers. As the name suggests, the probabilities are limited to 30 bit accuracy.
rng::discrete_distribution_30bit is about four times faster than rng::discrete_distribution when generating random deviates, but needs much longer for the initiation. Both classes are faster than std::discrete_distribution.
rng::well_1024: A uniform, 32 bit, psuedo random number generator with a period of 2^1024. The Well algorith thermalizes quicker than Matsumoto and Nishimura's Mercene twister. rng::well_1024 is faster than some implementations of std::mersenne_twister.
The directory ran_test contains a test program which demonstrates how to use the classes together with the C++11 framework for psuedo random number generation.