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Document Type |
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Thesis |
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Document Title |
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Distribution of The Extremes of Random Variables of Random Numbers توزيع القيم المتطرفة لمتغير عشوائي يحدث بعدد مرات متغيرة |
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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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Compound distributions can be useful in various fields such as failure time, reliability, life testing, risk theory, queuing theory, economic, extreme value theory and radar theory. Exact extreme value model one of the most important compound distributions which is based on the theory of the maximum of random variable of random numbers. This model uses partial series data to fit, analyze, and predict the largest flood peak discharge above a given base level concern a time interval [0, t], at a given location of a river. In this study, the theoretical considerations of exact extreme value model and its statistical properties are reviewed. A graphical description for the probability density function (PDF), the cumulative distribution function (CDF) and the hazard rate function (HRF) are discussed. Special cases and distributions related to the exact extreme value model are derived. To obtain the estimation of the unknown parameters, the moments (MOM), maximum likelihood (ML), and Bayesian methods based on non- informative and informative prior distributions have been used based on complete samples. The Markov Chain Monte Carlo (MCMC) technique has been used to calculate the Bayesian estimates based on squared error loss functions. Reliability function (RF) and HRF are estimated using these methods of estimation. The Monte Carlo simulation study is used to investigate and compare between the estimators for different sample sizes and different values for the parameters. The results of the simulation were provided using the program R. Comparing the mean squared error (MSE), the results showed that the Bayesian method based on informative prior distribution is the best estimation method.
A real data set is used to fit the model when the parameters are estimated by Bayesian method. The Kolmogorov-Smirnov (K-S) goodness of fit tests indicate that the compound model provides appropriate fit for this data set and it is more applicable than the same model when the parameters are estimated by ML method. |
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Supervisor |
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Dr. Neamat S.A. Qutb |
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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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Co-Supervisor |
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Dr. Aisha F.S. Fayomi |
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Added Date |
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Tuesday, July 11, 2017 |
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Researchers
| عهود ختام البلادي | AL- Beladi, Ohoud Kattam | Researcher | Master | |
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