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.
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