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Title: New Generalizations of Power Cauchy Distribution
Authors: Zubair, Muhammad
Keywords: Statistics
Issue Date: 2018
Publisher: Islamia University, Bahawalpur.
Abstract: Four new generalizations of power-Cauchy distribution are proposed in this thesis. Firstly, the Poisson-X family is proposed and its important mathematical properties are obtained. Then, a member of the Poisson-X family namely the Poisson power-Cauchy)distributionisdefinedanditsstructuralpropertiesareinvestigated. The proposed model is fitted to three real-life data sets to illustrate its flexibility. Secondly, the log-odd normal generalized family of distributions is introduced. Then, a special model of this family, the log-odd normal power-Cauchy is defined and its mathematical properties are obtained. A real-life data set is used to prove the superiority of the proposed model. Thirdly, the Weibull-Power-Cauchy distribution is proposed and its mathematical properties are obtained. Two useful characterizations based on truncated moments are also presented. The proposed model is applied to three real-life data sets to investigate its flexibility. Lastly, a new extensionofpower-Cauchymodelisproposedbycompoundingthepower-Cauchyand negative-binomial distribution called the power-Cauchy negative-binomial distribution. Some mathematical properties of the proposed model are obtained and the model parameters are estimated using the maximum likelihood method. A simulation study is carried out to investigate the performance of maximum likelihood method. The flexibility of the proposed model is illustrated through three real-life data sets. Then, a new class of regression model is introduced for location and scale based on the logarithm of the proposed random variable and, estimation and inference on the regression coefficients are discussed.
Gov't Doc #: 18683
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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