Kazuya Hayata
Department of Socio-Informatics, Sapporo Gakuin University, Ebetsu 069-8555, Japan
E-mail address: hayata1@hotmail.co.jp
(Received May 28, 2012; Accepted August 1, 2014)
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.
Keywords: Fibonacci Sequence, Golden Ratio, Golden Tree, Inverse Power Law, Word Spectrum