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On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization

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  • Piyapatr Busababodhin

    (Department of Mathematics, Mahasarakham University, Maha Sarakham 44150, Thailand
    Research Unit of Data Science and Sustainable Agriculture, Climate Change, Innovation and Extreme Risk Assessment (DSSA), Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand)

  • Tossapol Phoophiwfa

    (Department of Mathematics, Mahasarakham University, Maha Sarakham 44150, Thailand)

  • Andrei Volodin

    (Department of Mathematics and Statistics, University of Regina, Saskatchewan, SK S4S 0A2, Canada)

  • Sujitta Suraphee

    (Department of Mathematics, Mahasarakham University, Maha Sarakham 44150, Thailand)

Abstract

This study investigates the asymptotic properties of method-of-moments estimators for the Birnbaum–Saunders distribution under a newly proposed parametrization. Theoretical derivations establish the asymptotic normality of these estimators, supported by explicit expressions for the mean vector and variance–covariance matrix. Simulation studies validate these results across various sample sizes and parameter values. A practical application is demonstrated through modeling cumulative rainfall data from northeastern Thailand, highlighting the distribution’s suitability for extreme weather prediction.

Suggested Citation

  • Piyapatr Busababodhin & Tossapol Phoophiwfa & Andrei Volodin & Sujitta Suraphee, 2025. "On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization," Mathematics, MDPI, vol. 13(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:636-:d:1591676
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    References listed on IDEAS

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    1. Ng, H. K. T. & Kundu, D. & Balakrishnan, N., 2003. "Modified moment estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 283-298, July.
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