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CHECKERBOARD COPULAS OF MAXIMUM ENTROPY WITH PRESCRIBED MIXED MOMENTS

Part of: Combinatorics, graph theory, probability theory, statistics Communication, information

Published online by Cambridge University Press:  26 November 2018

JONATHAN BORWEIN  and
PHIL HOWLETT
JONATHAN BORWEIN
Affiliation:
(deceased), previously atSchool of Mathematical and Physical Sciences, CARMA, The University of Newcastle, Callaghan, NSW 2308, Australia
PHIL HOWLETT*
Affiliation:
Scheduling and Control Group (SCG), Centre for Industrial and Applied Mathematics (CIAM), School of Information Technology and Mathematical Sciences, University of South Australia, Australia email phil.howlett@unisa.edu.au
*
✉phil.howlett@unisa.edu.au
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Abstract

In modelling joint probability distributions it is often desirable to incorporate standard marginal distributions and match a set of key observed mixed moments. At the same time it may also be prudent to avoid additional unwarranted assumptions. The problem is to find the least ordered distribution that respects the prescribed constraints. In this paper we will construct a suitable joint probability distribution by finding the checkerboard copula of maximum entropy that allows us to incorporate the appropriate marginal distributions and match the nominated set of observed moments.

Keywords

joint probability distributionsmaximum entropyoptimizationconvex analysisFenchel duality

MSC classification

Primary: 97K80: Applied statistics
Secondary: 94A17: Measures of information, entropy 90C46: Optimality conditions, duality
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 3 , December 2019 , pp. 302 - 318
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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