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<p>In this article, we investigate the classical and Bayesian estimation of the Bonferroni Curve (BC) and Bonferroni Index (BI) under the Power Function Distribution. We derive the Maximum Likelihood Estimator and the Uniform Minimum Variance Unbiased Estimator in a classical setting and study their properties. Additionally, we explore the Bayesian estimator under the Squared Error Loss Function (SELF) and analyze its characteristics. The performance of these estimators is evaluated in terms of bias and variance under varying sample sizes through a Monte Carlo simulation. Additionally, real-world datasets are used to illustrate the performance of the proposed estimators.</p>

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Estimation of the Bonferroni Curve and Bonferroni Index for the power function distribution

  • 期刊论文

  • 发表日期：

    2025年8月9日

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  • E. I. Abdul Sathar,
  • Parvathy Sobhanan

摘要

In this article, we investigate the classical and Bayesian estimation of the Bonferroni Curve (BC) and Bonferroni Index (BI) under the Power Function Distribution. We derive the Maximum Likelihood Estimator and the Uniform Minimum Variance Unbiased Estimator in a classical setting and study their properties. Additionally, we explore the Bayesian estimator under the Squared Error Loss Function (SELF) and analyze its characteristics. The performance of these estimators is evaluated in terms of bias and variance under varying sample sizes through a Monte Carlo simulation. Additionally, real-world datasets are used to illustrate the performance of the proposed estimators.