Advances and Applications in Statistics
Volume 1, Issue 2, Pages 149 - 163
(August 2001)
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POWER-DIVERGENCE TYPE MEASURE OF DEPARTURE FROM AN ENTROPY MODEL
Sadao Tomizawa (Japan), Masahiko Sagae (Japan) and Makiko Uehara (Japan)
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Abstract: For one-dimensional discrete distribution, Kunisawa [An introduction to information theory for Or, Nikkagiken Press, Tokyo, 1959 (in Japanese); Entropy model, Nikkagiken Press, Tokyo, 1975 (in Japanese)] considered an entropy model under which a specific probability distribution maximizes the ratio of the Shannon entropy to the average category score, and applied the model to some marketing examples. Tomizawa, Sagae and Kunisawa [Japanese Journal of Applied Statistics 19 (1990), 183-187 (in Japanese); Mathematica Japonica 45 (1997), 39-42] considered two kinds of measures to represent the degree of departure from the entropy model. The purpose of this paper is to consider a generalization of Tomizawa, Sagae and Kunisawa’s measures. The measure proposed is expressed by using the power-divergence. An example is given. |
Keywords and phrases: extremal entropy, extremal mean, measure, power-divergence, Shannon entropy. |
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