Golden Distribution of Probabilities

Abstract

A novel concept based on the golden ratio φ, where the cumulative probability of the Fibonacci numbers coincides with the reciprocal of φ, is presented for discrete probability distributions. In addition to the binomial, Poisson, and geometrical distributions, the Benford-type as well as the inverse power distributions are considered. For the latter, in the limit of n → ∞ (n being a parameter of the present distribution), the value of the power is found to approach the fractal dimension of the golden tree. Finally, examples being close surprisingly to the golden distribution are shown for the analysis of the word spectra of texts written in English.