Closed-form parameter estimation for the bivariate gamma distribution: New approaches
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911152738402304 |
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| author | Vila, Roberto Saulo, Helton |
| author_facet | Vila, Roberto Saulo, Helton |
| contents | We propose new closed-form estimators for the parameters of McKay's bivariate gamma distribution by exploiting monotone transformations of the likelihood equations. As a special case, our framework recovers the estimators recently introduced by Zhao et al. (2022) [Zhao, J., Jang, Y.-H., and Kim, H. (2022). Closed-form and bias-corrected estimators for the bivariate gamma distribution. Journal of Multivariate Analysis, 191:105009]. Theoretical properties, including strong consistency and asymptotic normality, are established. We further introduce a second family of closed-form estimators that is explicitly built from the stochastic relationship between gamma random variables. Our second approach encompasses the estimators of Nawa and Nadarajah (2023) [Nawa, V. M. and Nadarajah, S. (2023). New closed form estimators for a bivariate gamma distribution. Statistics, 57(1):150-160]. Monte Carlo experiments are conducted to assess finite-sample performance, showing that the new estimators perform comparably to maximum likelihood estimators while avoiding iterative optimization, and improve upon the existing closed-form approach by Zhao et al. (2022) and Nawa and Nadarajah (2023). A real hydrological data set is analyzed to illustrate the proposed approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed-form parameter estimation for the bivariate gamma distribution: New approaches Vila, Roberto Saulo, Helton Methodology 60E05, 62Exx, 62Fxx We propose new closed-form estimators for the parameters of McKay's bivariate gamma distribution by exploiting monotone transformations of the likelihood equations. As a special case, our framework recovers the estimators recently introduced by Zhao et al. (2022) [Zhao, J., Jang, Y.-H., and Kim, H. (2022). Closed-form and bias-corrected estimators for the bivariate gamma distribution. Journal of Multivariate Analysis, 191:105009]. Theoretical properties, including strong consistency and asymptotic normality, are established. We further introduce a second family of closed-form estimators that is explicitly built from the stochastic relationship between gamma random variables. Our second approach encompasses the estimators of Nawa and Nadarajah (2023) [Nawa, V. M. and Nadarajah, S. (2023). New closed form estimators for a bivariate gamma distribution. Statistics, 57(1):150-160]. Monte Carlo experiments are conducted to assess finite-sample performance, showing that the new estimators perform comparably to maximum likelihood estimators while avoiding iterative optimization, and improve upon the existing closed-form approach by Zhao et al. (2022) and Nawa and Nadarajah (2023). A real hydrological data set is analyzed to illustrate the proposed approaches. |
| title | Closed-form parameter estimation for the bivariate gamma distribution: New approaches |
| topic | Methodology 60E05, 62Exx, 62Fxx |
| url | https://arxiv.org/abs/2509.10794 |