Wikanda Phaphan
ABSTRACT
Mixture generalized gamma distribution is a combination of two distributions -- Generalized gamma distribution and length biased generalized gamma distribution. This distribution is presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation -- maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 30, 100 and the simulation were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm.
- Diebold F.X., Rudebusch G.D. 1990. A Nonparametric investigation of duration dependence in the american business cycle. Journal of Political Economy. 98, 596--616.Google Scholar
Cross Ref
- Kiefer N.M. 1984. A simple test for heterogeneity in exponential models of duration. Journal of Labor Economics. 2, 539--549.Google ScholarCross Ref
- Favero C.A., Pesaran M.H., Sharma S. 1994. A duration model of irreversible oil investment: theory and empirical evidence. Journal of Applied Econometrics. 9, 95--112.Google ScholarCross Ref
- Eckstein Z., Wolpin K.I. 1995. Duration to first job and the return to schooling: estimates from a search-matching model. Review of Economic Studies. 62, 263--86.Google ScholarCross Ref
- Lancaster T. 1979. Econometric methods for the duration of unemployment. Econometrica. 47, 939--956.Google ScholarCross Ref
- R. L. Prentice 1975. Discrimination among some parametric models. Biometrika. 62,3, 607--614.Google ScholarCross Ref
- Gompertz, B. 1824. On the nature of the function expressive of the law of human mortality and on the new mode of determining the value of life contingencies. Phil. Trans. Royal Soc. A. 115, 513--580.Google Scholar
- Fisk, P.R. 1961. The Graduation of Income Distributions. Econometrica. 29,2,: 171--185.Google ScholarCross Ref
- Stacy, E.W. 1962. A generalization of the gamma distribution. Annals Mathem. Statist. 33, 1187--1192.Google ScholarCross Ref
- Suksaengrakcharoen, S. and Bodhisuwan, W. 2014. A new family of Generalized Gamma distribution and its application. J. Math. Stat. 10, 2, 211--220.Google ScholarCross Ref
- Minka, T. P. 2002. Estimating a Gamma distribution. https://tminka.github.io/papers/minka-gamma.pdfGoogle Scholar
- McLachlan, G.J. and Krishnan, T. 1997. The EM algorithm and extensions. Wiley and Sons, New York.Google Scholar
- Phaphan, W. and Budsaba, K. 2017. Parameter estimation of the crack lifetime distribution using the expectation-maximization algorithm. Far East Journal of Mathematical Science. 102, 5, 933--948.Google ScholarCross Ref
- Roddee, S. Chareonrum, S. Kumjit, S. and Phaphan, W. 2017. The generation of random variables having mixture generalized gamma distribution by the acceptance - rejection method. In Proceedings of the 5th Academic Science and Technology Conference 2017 (Miracle Grand Convention Hotel, May 25, 2017). Bangkok, Thailand 607--612.Google Scholar
Index Terms
- Estimating Parameter for the Mixture Generalized Gamma Distribution
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