Hurwitz-Riemann Zeta And Other Special Probability Distributions - AI Summary

All the solutions were probability distributions, and in this article we introduce an even larger, generic class of problems (chaotic discrete dynamical systems) with known solution. Each dynamical system discussed here (or in my previous article) comes with two distributions: The name Hurwitz and Riemann-Zeta is just a reminder of their strong connection to number theory problems such as continued fractions, approximation of irrational numbers by rational ones, the construction and distribution of the digits of random numbers in various numeration systems, and the famous Riemann Hypothesis that has a one million dollar prize attached to it. The most well known probability distribution related to these functions is the discrete Zipf distribution. The author defines a family of distribution that generalizes the exponential power, normal, gamma, Weibull, Rayleigh, Maxwell-Boltzmann and chi-squared distributions, with applications in actuarial sciences. Our Hurwitz-Riemann Zeta distribution is yet another example arising this time from discrete dynamical systems, continuous on [0, 1].