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Information measures of Dirichlet distribution with applications
Author(s) -
Ebrahimi Nader,
Soofi Ehsan S.,
Zhao Shaoqiong Annie
Publication year - 2011
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.870
Subject(s) - dirichlet distribution , mathematics , multinomial distribution , generalized dirichlet distribution , concentration parameter , categorical distribution , econometrics , dirichlet process , statistics , hierarchical dirichlet process , dirichlet series , probability distribution , mathematical analysis , bayesian probability , distribution fitting , inverse chi squared distribution , boundary value problem
We explore properties of information measures of the Dirichlet family and related distributions. Representations of the information measures of the Dirichlet family in terms of the information measures of the gamma family reflect the characterization of Dirichlet distribution in terms of the ratios of independent gamma distributions to their sum. We present measures of information provided by a multinomial vector about the multinomial parameters under the Dirichlet prior and measures of information loss due to aggregation of Dirichlet components and the multinomial categories. New information characterizations of the bivariate Dirichlet distribution in terms of survival and hazard gradient constraints are given. The information analysis of contingency tables is briefly described. An example illustrates applications of Dirichlet prior for inferences about information measures of contingency tables and Kendall's tau for ordinal data. Results that compare solicitation of the mean and mode vectors for the Dirichlet model are given and are illustrated through an example from a study of business executives' environmental uncertainty in the aftermath of 9/11 terrorist attacks. The probability integral transformation is proposed for facilitating implementation of the maximum entropy Dirichlet process prior procedure for inference about the fit of continuous distributions to the data. Copyright © 2011 John Wiley & Sons, Ltd.