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Modified Kibria–Lukman Estimator for the Conway–Maxwell–Poisson Regression Model: Simulation and Application

Author

Listed:
  • Nasser A. Alreshidi

    (Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia)

  • Masad A. Alrasheedi

    (Department of Management Information Systems, College of Business Administration, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia)

  • Adewale F. Lukman

    (Department of Mathematics and Statistics, University of North Dakota, Grand Forks, ND 58202, USA)

  • Hleil Alrweili

    (Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia)

  • Rasha A. Farghali

    (Department of Mathematics, Insurance and Applied Statistics, Helwan University, Cairo 11795, Egypt)

Abstract

This study presents a novel estimator that combines the Kibria–Lukman and ridge estimators to address the challenges of multicollinearity in Conway–Maxwell–Poisson (COMP) regression models. The Conventional COMP Maximum Likelihood Estimator (CMLE) is notably susceptible to the adverse effects of multicollinearity, underscoring the necessity for alternative estimation strategies. We comprehensively compare the proposed COMP Modified Kibria–Lukman estimator (CMKLE) against existing methodologies to mitigate multicollinearity effects. Through rigorous Monte Carlo simulations and real-world applications, our results demonstrate that the CMKLE exhibits superior resilience to multicollinearity while consistently achieving lower mean squared error (MSE) values. Additionally, our findings underscore the critical role of larger sample sizes in enhancing estimator performance, particularly in the presence of high multicollinearity and over-dispersion. Importantly, the CMKLE outperforms traditional estimators, including the CMLE, in predictive accuracy, reinforcing the imperative for judicious selection of estimation techniques in statistical modeling.

Suggested Citation

  • Nasser A. Alreshidi & Masad A. Alrasheedi & Adewale F. Lukman & Hleil Alrweili & Rasha A. Farghali, 2025. "Modified Kibria–Lukman Estimator for the Conway–Maxwell–Poisson Regression Model: Simulation and Application," Mathematics, MDPI, vol. 13(5), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:794-:d:1601652
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    References listed on IDEAS

    as
    1. Sellers, Kimberly F. & Raim, Andrew, 2016. "A flexible zero-inflated model to address data dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 68-80.
    2. Chatla, Suneel Babu & Shmueli, Galit, 2018. "Efficient estimation of COM–Poisson regression and a generalized additive model," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 71-88.
    3. Adewale F. Lukman & Olayan Albalawi & Mohammad Arashi & Jeza Allohibi & Abdulmajeed Atiah Alharbi & Rasha A. Farghali, 2024. "Robust Negative Binomial Regression via the Kibria–Lukman Strategy: Methodology and Application," Mathematics, MDPI, vol. 12(18), pages 1-16, September.
    4. Muhammad Nauman Akram & Muhammad Amin & Faiza Sami & Adam Braima Mastor & Omer Mohamed Egeh & Abdisalam Hassan Muse & Georgios Psarrakos, 2022. "A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, March.
    5. Royce A. Francis & Srinivas Reddy Geedipally & Seth D. Guikema & Soma Sekhar Dhavala & Dominique Lord & Sarah LaRocca, 2012. "Characterizing the Performance of the Conway‐Maxwell Poisson Generalized Linear Model," Risk Analysis, John Wiley & Sons, vol. 32(1), pages 167-183, January.
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