Regular Article

Bivariate superstatistics based on generalized gamma distribution

¹ Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción, Chile
² Instituto de Investigación Multidisciplinario en Ciencia y Tecnología, Universidad de La Serena, La Serena, Chile

^a e-mail: chcaaman@ubiobio.cl

Received: 17 December 2019
Received in final form: 1 February 2020
Published online: 4 March 2020

Abstract

The univariate gamma (chi-squared) superstatistics has been used in several applications by assuming independence between systems. However, in some cases it seems more reasonable to consider a dependence structure. This fact motivates the introduction of a family of bivariate superstatistics based on an extension of the gamma distribution, defined by generalized hypergeometric functions. The particular cases include Boltzmann and other statistical weighting factors in the literature. Numerical illustrations show the behaviour of the proposed superstatistics.