Variants of Mixtures: Information Properties and Applications

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.

Option pricing with maximum entropy densities: The inclusion of higher‐order moments

“…First, this approach can be applied to any assets without the restrictions of the parametric methods. Second, the ME density is flexible to capture multimodality and mixture models (Ardakani et al, 2021). Third, the inclusion of higher-order moment constraints in the ME problem provides sufficient information for estimating the RN density.…”