Open AccessSome Distributions Associated with Bose-Einstein Statistics
Author(s) -
Yuji Ijiri,
Herbert A. Simon
Publication year - 1975
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.72.5.1654
Subject(s) - statistics , mathematics , statistical physics , event (particle physics) , distribution (mathematics) , einstein , pareto principle , pareto distribution , limiting , boundary (topology) , stochastic process , physics , mathematical analysis , mathematical physics , quantum mechanics , mechanical engineering , engineering
This paper examines a stochastic process for Bose-Einstein statistics that is based on Gibrat's Law (roughly: the probability of a new occurrence of an event is proportional to the number of times it has occurred previously). From the necessary conditions for the steady state of the process are derived, under two slightly different sets of boundary conditions, the geometric distribution and the Yule distribution, respectively. The latter derivation provides a simpler method than the one earlier proposed by Hill [J. Amer. Statist. Ass. (1974) 69, 1017-1026] for obtaining the Pareto Law (a limiting case of the Yule distribution) from Bose-Einstein statistics. The stochastic process is applied to the phenomena of city sizes and growth.