On some weighted distributions and their bivariate extension / Hagar Mohamed Abdelghany Azab ; Supervised Hiba Zeyada Muhammed

Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Mathematical Statistics

Rayleigh (R) distribution has wide application in several real life situations particularly, reliability analysis, medicines, life testing etc. A new version of weighted Rayleigh distribution named the modified weighted Rayleigh (MWR) distribution is constructed and studied. The statistical properties of the MWR distribution including the behavior of hazard and reversed hazard functions, moments, the central moments, moment generating function, mean, variance, coefficient of skewness, coefficient of kurtosis, median, mode, quantile, stochastic ordering, exact information matrix and order statistics are obtained, a simulation study and real data applications are performed. Moreover, a bivariate extension of the MWR distribution named the bivariate modified Rayleigh (BMWR) distribution is introduced. The proposed bivariate distribution is of type Farlie{u2013}Gumbel{u2013}Morgenstern (FGM) copula. The BMWR distribution has modified weighted Rayleigh marginal distributions. The joint cumulative distribution function, the joint survival function, the joint probability density function, the joint hazard function and the statistical properties of the BMWR distribution are also derived. Real data set has been introduced and analyzed to examine the model applicability Uniform (U) distribution is regarded at the simplest probability model with bounded support. We introduced a new version of this distribution which is called the modified weighted uniform (MWU) distribution. Some mathematical properties of MWU distribution including cumulative distribution function, moments, median, quantiles, mode, reliability measures as survival function and hazard function, stochastic order and the order statistics have been derived. Parameters of the MWU distribution are estimated by method of moments (MOM) and maximum likelihood (ML). An application of the MWU distribution is provided for life time data set. Kolmogorov Smirnov (K-S) test statistic, AIC and BIC are applied to check the model fitting, a simulation study is also performed

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