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<p>Parameter estimation is crucial for statistical analysis as it forms the basis for inference, prediction, and decision-making. This study compares various methods for parameters estimation of the Bivariate Affine Linear Exponential (BALE) distribution, which is adept at modeling moderate dependence structures between variables and competent for further generalization. We compare different estimation methods, including maximum likelihood (ML), least squares (LS), weighted least squares (WLS), relative least squares (RLS) and Bayesian estimation through Monte Carlo simulations across various parameter values and sample sizes. These parameter estimation methods are then evaluated on the bases of bias, standard errors, total mean square error (TMSE) and root mean square error (RMSE) as performance metrics. To ensure practical relevance, applicability along with the validity of simulation results, these methods are applied to real-life cardiorenal disease data.</p>

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Identifying the Optimal Parameter Estimation Method for Bivariate Affine Linear Exponential Distribution with an Application to Cardiorenal Disease Data

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Soban Ahmad,
  • Muhammad Mohsin,
  • Sajjad Haider Bhatti

摘要

Parameter estimation is crucial for statistical analysis as it forms the basis for inference, prediction, and decision-making. This study compares various methods for parameters estimation of the Bivariate Affine Linear Exponential (BALE) distribution, which is adept at modeling moderate dependence structures between variables and competent for further generalization. We compare different estimation methods, including maximum likelihood (ML), least squares (LS), weighted least squares (WLS), relative least squares (RLS) and Bayesian estimation through Monte Carlo simulations across various parameter values and sample sizes. These parameter estimation methods are then evaluated on the bases of bias, standard errors, total mean square error (TMSE) and root mean square error (RMSE) as performance metrics. To ensure practical relevance, applicability along with the validity of simulation results, these methods are applied to real-life cardiorenal disease data.