On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization
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 v...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/4/636 |
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| author | Piyapatr Busababodhin Tossapol Phoophiwfa Andrei Volodin Sujitta Suraphee |
| author_facet | Piyapatr Busababodhin Tossapol Phoophiwfa Andrei Volodin Sujitta Suraphee |
| author_sort | Piyapatr Busababodhin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3381fc04a1014ff4b5bd19ecbea81b2f |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-3381fc04a1014ff4b5bd19ecbea81b2f2025-08-20T02:03:31ZengMDPI AGMathematics2227-73902025-02-0113463610.3390/math13040636On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New ParametrizationPiyapatr Busababodhin0Tossapol Phoophiwfa1Andrei Volodin2Sujitta Suraphee3Department of Mathematics, Mahasarakham University, Maha Sarakham 44150, ThailandDepartment of Mathematics, Mahasarakham University, Maha Sarakham 44150, ThailandDepartment of Mathematics and Statistics, University of Regina, Saskatchewan, SK S4S 0A2, CanadaDepartment of Mathematics, Mahasarakham University, Maha Sarakham 44150, ThailandThis 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.https://www.mdpi.com/2227-7390/13/4/636Birnbaum–Saunders distributionmethod of moments estimationasymptotic normalitydelta methodreturn level |
| spellingShingle | Piyapatr Busababodhin Tossapol Phoophiwfa Andrei Volodin Sujitta Suraphee On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization Mathematics Birnbaum–Saunders distribution method of moments estimation asymptotic normality delta method return level |
| title | On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization |
| title_full | On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization |
| title_fullStr | On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization |
| title_full_unstemmed | On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization |
| title_short | On the Asymptotic Normality of the Method of Moments Estimators for the Birnbaum–Saunders Distribution with a New Parametrization |
| title_sort | on the asymptotic normality of the method of moments estimators for the birnbaum saunders distribution with a new parametrization |
| topic | Birnbaum–Saunders distribution method of moments estimation asymptotic normality delta method return level |
| url | https://www.mdpi.com/2227-7390/13/4/636 |
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