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A generalization of Marshall-Olkin bivariate Pareto model and its applications in shock and competing risk models | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 7، دوره 1، شماره 1، اردیبهشت 2020، صفحه 69-87 اصل مقاله (655.49 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2018.14869.1012 | ||
| نویسندگان | ||
| Shirin Shoaee* 1؛ Esmaeil Khorram2 | ||
| 1Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran | ||
| 2Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran | ||
| چکیده | ||
| Statistical inference for extremes has been a subject of intensive research during the last years. In this paper, we generalize the Marshall-Olkin bivariate Pareto distribution. In this case, a new bivariate distribution is introduced by compounding the Pareto Type $\rm{II}$ and geometric distributions. This new bivariate distribution has natural interpretations and can be applied in fatal shock models or in competing risks models. We call the new proposed model Marshall-Olkin bivariate Pareto-geometric (MOBPG) distribution, and then investigate various properties of the new distribution. This model has five unknown parameters and the maximum likelihood estimators cannot be afforded in explicit structure. We suggest to use the EM algorithm to calculate the maximum likelihood estimators of the unknown parameters, and this structure is quite flexible. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze a real data set to investigate our purposes. | ||
| کلیدواژه‌ها | ||
| Bivariate model؛ Competing risk model؛ Expectation-Maximization algorithm؛ Pareto Type $\rm{II}$ distribution؛ Shock model | ||
| مراجع | ||
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