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<p>This paper investigates and extends the Generalized binomial distribution (GBD) as a novel extension of the classical binomial distribution designed to model dynamic feedback dependencies commonly encountered in decision-making contexts. By adjusting success probabilities based on prior outcomes, the GBD addresses critical limitations of traditional binomial and beta-binomial models, such as underestimating variance and failing to capture complex behaviors like bi-modality. Through extensive simulation studies and real-world applications, including marketing optimization and stock performance analysis, we demonstrate the versatility of the GBD in capturing feedback-driven phenomena. We also provide interactive tools (dashboards) to facilitate parameter exploration and practical implementation. These findings establish GBD as a valuable analytical tool for decision-making in management and operations offering both enhanced interpretability and actionable insights while retaining the simplicity of classical binomial frameworks.</p>

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Generalized binomial models for analytics and decision-making: capturing feedback dependencies

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Zvi Drezner,
  • Dawit Zerom

摘要

This paper investigates and extends the Generalized binomial distribution (GBD) as a novel extension of the classical binomial distribution designed to model dynamic feedback dependencies commonly encountered in decision-making contexts. By adjusting success probabilities based on prior outcomes, the GBD addresses critical limitations of traditional binomial and beta-binomial models, such as underestimating variance and failing to capture complex behaviors like bi-modality. Through extensive simulation studies and real-world applications, including marketing optimization and stock performance analysis, we demonstrate the versatility of the GBD in capturing feedback-driven phenomena. We also provide interactive tools (dashboards) to facilitate parameter exploration and practical implementation. These findings establish GBD as a valuable analytical tool for decision-making in management and operations offering both enhanced interpretability and actionable insights while retaining the simplicity of classical binomial frameworks.