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Document Type |
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Thesis |
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Document Title |
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FURTHER CONTRIBUTION TO THE PROBLEMS OF ESTIMATION IN SOME PROBABILISTIC MODELS مزيداً من الإسهامات نحو مسائل التقدير في بعض النماذج الاحصائية |
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Subject |
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Faculty of Sciences |
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Document Language |
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Arabic |
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Abstract |
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This work lies in the area of Statistical Inferences which is deemed to be one of the most popular areas of statistics. Probabilistic models are based on probability theory and are widely used in many applications in different fields of science. In a probabilistic model, the measured data is assumed to be random with a specific distribution dependent on the parameters of interest. It turns out that the estimation problem is very essential and critical in statistical inferences.
We consider different methods of estimation of the unknown parameters of a three-parameter Dagum distribution. Various mathematical and statistical properties of the Dagum distribution are derived. We describe different frequentist approaches; namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, maximum product of spacing estimators, minimum distances estimators, Cram´er-von-Mises estimators, Anderson-Darling and right-tail Anderson-Darling estimators. Monte Carlo simulations are performed to compare the performances of the used methods for small and large samples. Also, a real data set has been analyzed for illustrative purposes.
Moreover, the problem of estimating the reliability of a single and multicomponent stress-strength is considered. We obtain the maximum likelihood estimators and the Bayes estimators of R = P(Y < X) when X and Y are two independent random variables following Dagum distribution. Also, the reliability of a multicomponent stress-strength model is estimated using the maximum likelihood. Consequently, the asymptotic confidence intervals of the reliability of a single and multicomponent stress-strength model are constructed. Gibbs and Metropolis-Hastings sampling was used to provide sample-based estimates of the reliability and its associated credible intervals. For illustrative purposes, Monte Carlo simulations are carried out. |
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Supervisor |
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Dr. Bander Al-Zahrani |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1438 AH
2017 AD |
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Added Date |
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Thursday, June 8, 2017 |
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Researchers
| سميرة صالح باسلوم | Bsloom, Samerah Saleh | Researcher | Master | |
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