Abstract
AbstractWhen the cells are ordinal in the multinomial distribution, i.e., when cells have a natural ordering, guaranteeing that the borrowing information among neighboring cells makes sense conceptually. In this paper, we introduce a novel probability distribution for borrowing information among neighboring cells in order to provide reliable estimates for cell probabilities. The proposed smoothed Dirichlet distribution forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet distribution. Basic properties of the proposed distribution, including normalizing constant, moments, and marginal distributions, are developed. Sample generation of smoothed Dirichlet distribution is discussed using the acceptance-rejection algorithm. We demonstrate the performance of the proposed smoothed Dirichlet distribution using 2018 Major League Baseball (MLB) batters data.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computer Science Applications,Statistics and Probability
Reference11 articles.
1. Guardiola, J.H.: The spherical-Dirichlet distribution. J Stat Distrib Appl (2020). https://doi.org/10.1186/s40488-020-00106-9
2. Hjort, N. L.: Bayesian Statistics 5, Chapter Bayesian approaches to non- and semi-parametric density estimation, pp. 223–254, (1996)
3. Najar, F., Bouguila, N.: Image categorization using agglomerative clustering based smoothed Dirichlet mixtures. In: Yen, Y. (ed.) Advances in visual computing, pp. 27–38. Springer International Publishing (2020)
4. Nallapati, R.: The Smoothed Dirichlet Distribution: Understanding Cross-Entropy Ranking in Information Retrieval. Ph. D. thesis (2006)
5. Ng, K.W., Tang, M., Tan, M., Tian, G.: Grouped Dirichlet distribution: a new tool for incomplete categorical data analysis. J Multivar Anal 99(3), 490–509 (2008)
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