Estimating the Parameters of Mixture Gamma Distributions Using Maximum Likelihood and Bayesian Method
Section: Research Paper
Abstract
This paper focuses on the mixture Gamma distribution and uses the maximum likelihood and Bayesian techniques to estimate its parameters. This study uses Expectation Maximization Algorithm (EM) to find the maximum likelihood estimators and the random Metropolis-Hastings algorithm is used to simulate the Bayesian estimates of the parameters of mixture gamma distribution. then these estimates are compared by using the sum of the modulus of the bias (MBias), and the root-mean square error (RMSE). It has been shown that the Bayesian estimator is better than the maximum likelihood estimator.
References
- Al-masri, Hanin, s,. (2020).Bayesian inference on the genralized gamma distrbution. Journal of natural studies, Islamic university of gaza, V(28), pp 01-18.
- Chris, F., & Raftery, A,. (2017). Model-based clustering, discriminant analysis, and density estimation. Journal of the American statistical Association, 5(1).
- Corduneanu, A. & Bishop, C.M. (2001), Variational bayesian model selection for mixture distrbution , Artifitial intellegence and statistics, T. Jaakkola and T. Richardson (Eds) pp 27-34, Morgan Kaufmann.
- Dempster AP, Laird NM, Rubin DB. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. B 39:138
- Filho, I. (2008). "Mixture Models for the Analysis of Gene Expression: Integration of Multiple Experiments and Cluster Validation. Berlin, Germany: Department of Mathematics and Computer Science, Free University of Berlin, GermanyPatwray, A. N.; Sriwastav, G. L.; Hazarika, J. "Inference of R= P (X< Y
- Friedman, J., Hastie, T., and Tibshirani, R. (2009). The elements of statistical learning,, Springer series in statistics , New york, Vol 2.
- Ghojogh, B., Ghojogh, A., Crowley, M., and Karray, F. (2019). Fitting a mixture distrbution to data , Waterloo, canada.
- Jewell NP. (1982).Mixtures of exponential distributions. Ann Stat.; 10(2): 479-484.
- Jose M Bernardo and Adrian FM Smith.. (1982) Bayesian theory. volume 405 of Wiley Series in Probability and Statistics. John Wiley & Sons, 2009.
- Li L.A., Decomposition Theorems,.( 1983), Conditional Probability, and Finite Mixtures Distributions. PhD Thesis, State University, Albany, New York,.
- Newcomb S. (1886). A generalized theory of the combination of observations so as to obtain the best result).Am. J. Math. 8:34366
- Saieed, H,A.(2005) Estimation 0f parameters of mixture distributions and Its application on Neonatal birth weight data in Nineveh Govemorate, Unpublished doctors thesis , college of computer Science and Mathematics , University of .
- Sattaytham, P. and Talangtam, T.(2012). Fitting of finite mixture distrbutions to motor insurance claims. Journal of mathematics and statistics, 8(1), pp 49-56.
- SK Upadhyay, N Vasishta, and AFM Smith(2000). Bayes inference in life testing and reliability via markov chain monte carlo simulation. Sankhya: The Indian Journal of Statistics, Series A, pages 203{222.
- Valieris ,R. , Drummond,R.D., Defelicibns , A. , Dias-Neto , E., Rosales, R.A.& da Silva, I.T. A mixture model for determining SARS-COV-2 varint composition in pooled samples, Universidade de sao paulo, Ribeirao, sao paulo 14040-901, Barazil.
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Abd Al-Aziz Al-Talib, B., & Ibrahim Abdulla Najm, N. (2025). Estimating the Parameters of Mixture Gamma Distributions Using Maximum Likelihood and Bayesian Method. IRAQI JOURNAL OF STATISTICAL SCIENCES, 21(1), 138–150. Retrieved from https://rjps.uomosul.edu.iq/index.php/stats/article/view/20595
