Bayesian analysis of heterogeneous data outliers using a censored mixture model

Nadeem Akhtar () and Muteb Faraj Alharthi ()
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Nadeem Akhtar: Islamia College Peshawar
Muteb Faraj Alharthi: Taif University

Statistical Papers, 2025, vol. 66, issue 3, No 6, 17 pages

Abstract: Abstract This research introduces a new model for analyzing fluctuating data, such as coronavirus case counts, which typically start with small numbers and spike during colder weather, leading to increased hospital admissions. This way the model is capable of capturing the middle data while removing the outliers at specific intervals and is capable of being efficient and accurate. This approach efficiently deals with heterogenic data, for example, males and females affected by coronavirus, which confirms the readiness and adaptability of the model. Based on this framework, we explore the Bayesian approach for estimating unknown parameters using doubly type-I censoring for a two-component mixture of geometric distributions. The expression of Bayes estimators (BEs) and Bayes risks (BRs) are derived under the Kumaraswamy prior, utilizing four distinct loss functions: the squared error loss function (SELF), the DeGroot loss function (DLF), the quadratic loss function (QLF), and the precautionary loss function (PLF). The use of the Kumaraswamy prior enhances flexibility in modeling parameter uncertainty and variability, further strengthening the model’s effectiveness. To assess the performance of the proposed estimators, a Monte Carlo simulation is conducted. Additionally, a real-world data application is provided to demonstrate the practical utility of the approach. Both the Monte Carlo simulation and real-data analysis reveal that the Square Loss Function (SELF) consistently provides more accurate parameter estimates, highlighting the strength of this method in capturing essential data patterns and delivering reliable results.

Keywords: Geometric distribution; Kumaraswamy prior; Posterior distribution; Marginal distribution; Bayes estimators; Bayes risks; Loss functions (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-024-01638-x

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