Document Details
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Document Type |
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Thesis |
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Document Title |
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Extended Method to Generate Families of Distributions طريقة موسعة لتوليد عوائل من التوزيعات |
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Subject |
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Faculty of Science |
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Document Language |
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Arabic |
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Abstract |
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Many statistical distributions have been extensively applied over the past decades for describing and predicting real-world phenomena. These distributions have been applied in several disciplines such as economics, engineering, finance, insurance, demography, biology, environmental and medical sciences. However, in many of these areas, the data usually exhibit complicated behavior and varied shapes associated with various degrees of skewness and kurtosis. Many of the existing standard distributions have some limitations to fit these data accurately and applying these classical distributions could not provide an acceptable fit.
Therefore, the main aim of this thesis is trying to extend and modify some of the existing classical distributions in order to obtain greater flexibility and adaptability in modeling data from different fields of study. Specifically, this thesis introduces three novel techniques for constructing families that generate new distributions with more flexibility and adaptability in fitting data. The first method combines two well-known techniques for generating distributions: the transformed-transformer and the alpha power transformation. This new approach is applied to introduce two new distributions: namely, the alpha power Weibull-exponential and alpha power Topp-Leone Dagum. Next, the second method is introduced, which combines three well-known techniques for generating distributions: the transformed-transformer, exponentiated, and the alpha power transformation. This new approach is applied to introduce the new distribution: namely, the alpha power exponentiated new Weibull-Pareto.
Furthermore, the alpha power exponentiated Weibull-exponential distribution is introduced based on the third approach for generating distributions, which combines two families of distributions called the exponentiated transformed-transformer and the alpha power transformation.
For each of these new distributions, some significant mathematical features are studied. These features include the moments, quantile function, skewness, kurtosis, median, mean residual life, order statistics, and entropy. The inferential method of maximum likelihood is employed to estimate the unknown parameters of the proposed distributions. These estimates are evaluated based on various simulation studies. Moreover, the usefulness of each model is investigated by means of some applications to real data sets.
Overall, the results indicate that the density and the hazard rate functions of these members of the proposed families take a great diversity of shapes. Hence, it can be concluded that these novel families can offer great flexibility in modeling real data. Subsequently, its member can better fit the data when compared to other competing distributions. |
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Supervisor |
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Dr. Lamya Baharith |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1443 AH
2022 AD |
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Co-Supervisor |
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Dr. Hadeel Klakattawi |
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Added Date |
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Wednesday, January 25, 2023 |
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Researchers
| وداد حماد الجهني | Al-juhani, Wedad Hammad | Researcher | Master | |
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