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arXiv · 2509.10794

Closed-form parameter estimation for the bivariate gamma distribution: New approaches

Roberto Vila·Helton Saulo
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Abstract

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.

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Roberto Vila, Helton Saulo. 2025-09-13. Closed-form parameter estimation for the bivariate gamma distribution: New approaches. https://arxiv.org/abs/2509.10794

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