Document Details
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Document Type |
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Thesis |
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Document Title |
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GENERAL TRANSMUTED FAMILIES OF DISTRIBUTIONS AND RELATED RESULTS عائلات عامة من التوزيعات المحولة والنتائج المتعلقة بها |
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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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Transmutation map is the functional composition of the cumulative distribution function of one distribution with the inverse cumulative distribution (quantile) function of another. Actually, transmutation map is a convenient way of obtaining new probability distributions. Transmuted probability distributions are available in literature to handle the uni-modal data. Capturing the complex behavior of the data theoretical development in the area of transmuted distributions is very much essential.
In this research, two general transmutation approaches have been introduced to develop general transmuted families of distributions and special emphasis has been given to the cubic transmuted families of distributions. Several cubic transmuted distributions like cubic transmuted exponential, cubic transmuted Weibull and cubic transmuted Pareto have been developed using two proposed families. Distributional properties like moments, characteristic function, quantile function, reliability function, hazard rate function, random number generation and Shannon entropy have been studied. The maximum likelihood estimators of the model parameters has been obtained for the proposed distributions. Simulation study has been conducted to observe the performance of estimation procedures. It has been observed that the mean square errors decreases remarkably with increase in the sample size. This shows the consistency of estimates for all the proposed probability distributions.
In order to investigate the applicability of the proposed cubic transmuted models, some real-life data sets have been considered. Several goodness of fit criteria like log-likelihood, Akaike’s information criterion, corrected Akaike’s information criterion, Bayesian information criterion, Kolmogorov-Smirnov statistic, Anderson-Darling statistic and Cramér-von Mises statistic have been used to decide about goodness of fit of the proposed models for the real data sets.
It has been observed that the proposed cubic transmuted distributions fits the data sets reasonably well as compared with the competing distributions.
Keywords: General Transmutation, Cubic Transmuted Distributions, Exponential Distribution, Weibull Distribution, Pareto Distribution, Probability weighted moment, Maximum Likelihood Estimation, Reliability Analysis. |
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Supervisor |
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Prof. Dr. Muhammad Qaiser Shahbaz |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1440 AH
2019 AD |
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Co-Supervisor |
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Prof. Bander Al-Zahrani |
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Added Date |
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Monday, March 4, 2019 |
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Researchers
| مد محبوبور رحمن | Rahman, Md Mahabubur | Researcher | Doctorate | |
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