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

Piyapatr Busababodhin, Tossapol Phoophiwfa, Andrei Volodin () and Sujitta Suraphee
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Piyapatr Busababodhin: Department of Mathematics, 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

Mathematics, 2025, vol. 13, issue 4, 1-17

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.

Keywords: Birnbaum–Saunders distribution; method of moments estimation; asymptotic normality; delta method; return level (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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