Generalized entropy optimization problems with finite moment function sets

Shamilov A.

JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS, vol.13, no.3, pp.595-603, 2010 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 3
  • Publication Date: 2010
  • Doi Number: 10.1080/09720510.2010.10701489
  • Journal Name: JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.595-603
  • Keywords: MaxMaxEnt, MinMaxEnt distributions, generalized entropy optimization problem, finite moment function set
  • Anadolu University Affiliated: Yes

Abstract

In the present study we investigated generalized entropy optimization problem (GEOP) with finite moment functions set. On the set of combinations of this set we have obtained MaxMaxEnt and MinMaxEnt entropy optimization distributions (EOD) as a solution of GEOP. It is proved that by increasing the number of elements of combinations MaxMaxEnt and MinMaxEnt distributions became closer to given statistical data in the EO measure. This property together with others allows formulating a criterion to compare various moment function sets in suitability for statistical data. The established results allow considering GEOP even in the case when the moment functions number is greater than the number of the probability distribution components. Moreover, the best acceptable set of moment function combinations for given statistical data is indicated.