97-36:FDOD Function and the Information Discrepancy Contained in Multiple Probability Distributions

DIMACS TR: 97-36

FDOD Function and the Information Discrepancy Contained in Multiple Probability Distributions

Author:Weiwu Fang

ABSTRACT
The concept of Shannon information has played a significant role in a variety of scientific and engineering areas. The question naturally arises: how can we measure information discrepancy contained in two or more probability distributions? The answer to this problem will be very interesting in both theory and practice. Some measures for the cases of two or three distributions have presented by the pioneers, but these measures have some disadvantages; moreover, there doesn't exist a measure for $n$ distributions so far.

A FDOD function with many good properties has been introduced in the study of information discrepancy of judgments of multiple experts ( FW 1994). In this paper, based on the ideas concerned with Shannon information and measures of difference, we propose an axiom set for measuring the information discrepancy contained in a group of distributions, and prove that the only function satisfying the axiom set is of the FDOD form. The final results and even the intermediate results in deed show the close connection of the FDOD function with Shannon information and the measures of difference in statistics.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-36.ps.gz

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