Document Type
Article
Publication Date
2021
Publication Title
Journal of the Iranian Statistical Society
DOI
10.52547/jirss.20.1.27
Abstract
In recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in different fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic view of these studies and provides further insights and examples. We note that the insightful probabilistic formulation of the mixing parameters stipulated by Behboodian (1972) is required for a representation of the well-known information measure of the arithmetic mixture. Applications of this information measure presented in this paper include lifetime modeling, system reliability, measuring uncertainty and disagreement of forecasters, probability modeling with partial information, and information loss of kernel estimation. Probabilistic formulations of the mixing weights for various types of mixtures provide the Bayes-Fisher information and the Bayes risk of the mean residual function.
Recommended Citation
Ardakani, Omid, Majid Asadi, Nader Ebrahimi, Ehsan Soofi.
2021.
"Variants of Mixtures: Information Properties and Applications."
Journal of the Iranian Statistical Society, 20 (1): 27-59: Iranian Statistical Society.
doi: 10.52547/jirss.20.1.27 source: http://jirss.irstat.ir/article-1-775-en.html
https://digitalcommons.georgiasouthern.edu/economics-facpubs/185
Copyright
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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