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Document Type |
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Thesis |
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Document Title |
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On Bayesian Inferences for the Finite Mixture of Burr Type XII Distribution and its Reciprocal حول استدلالات بييز لخليط محدود من توزيع بير الثاني عشر ومقلوبه |
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Subject |
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Statistics department |
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Document Language |
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Arabic |
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Abstract |
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The Burr distribution is an important model in many fields such as business, engineering, quality control and other fields. Further, the Burr distribution having logistic and Weibull as special sub-models, is a very popular distribution for modeling lifetime data and for modeling phenomenon with monotone failure rates. Moreover, the mixtures of distributions are many interesting in various scientific fields such as physics, biology and medicine among others.
In this Thesis, the finite mixture model consisting of the Burr type XII and its reciprocal which is actually the Burr type III is considered with mixing proportions and two shape parameters. It is worth mentioning that this model, which is simply denoted by MBR, have been proposed by Ahmad, Jaheen and Mohamed (2011a). Also, the MBR is considered under generalized order statistics and then specified the results to upper record values and progressive type II censored sample.
The main objective of this study is to obtain estimation of the unknown parameters, reliability and hazard rate functions of the finite mixture model based on generalized order statistics. The maximum likelihood and Bayes methods based on squared error and linear-exponential loss functions have been used. Also, the Bayesian prediction for future observations from the finite mixture model are considered when the informative and future samples are from generalized order statistic by using one-sample and two-sample prediction techniques.
Moreover, the results obtained for MBR based on generalized order statistics have been specified to upper record values and progressive type II censored sample. The Monte Carlo integration technique has been used to obtain Bayes estimates. Further, the Monte Carlo simulation study is used to investigate and compare the maximum likelihood and Bayes estimates for different sample sizes, different sizes of record values and different censoring schemes. In conclusion, the Bayes estimates are more efficient than maximum likelihood estimates in many situations. Finally, the numerical examples are obtained to illustrate the prediction methods. Further, the results for MBR based on generalized order statistics can be specified to any other special cases (Kamps (1995)). |
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Supervisor |
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Dr. Zeinhum Fekri Jaheen |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1433 AH
2012 AD |
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Co-Supervisor |
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Dr. Samia Abbas Adhm |
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Added Date |
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Sunday, November 18, 2012 |
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Researchers
| تهاني أحمد بصير | Baseer, Tahani Ahmad | Researcher | Master | |
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