Estimation and discrimination of the bivariate marshall-olkin family / Ola Alsayed Mohamed Hussin Abuelamayem ; Supervised Hanan M. Aly

Thesis (Ph.D.) - Cairo University - Faculty of Economics and Political Science - Department of Statistics

Global competition in companion with using higher manufacturing technologies resulted in producing multi-components products. To test the reliability of these products and to determine their lifetime, univariate distributions will not be sufficient.This led to the use of bivariate and multivariate distributions in reliability engineering. To keep up with scientific development, different bivariate lifetime families were constructed and used in reliability engineering. Bivariate Marshll-Olkin family is commonly used in survival analysis as it takes into consideration all different scenarios of the random variables (i.e. the first random variable is smaller, greater or equal to the second random variable). In this thesis, we derive bivariate inverted Kumaraswamy distribution as a new member in the bivariate Marshall-Olkin family. Several properties such as marginal and conditional distributions, moment generating function and product moments are derived. Also, estimates of the unknown parameters are obtained using maximum likelihood and Bayesian approaches.Since there is a lot of lifetime distributions, one may find out that two or more distributions fit the data well, so the question is which one should we choose? This leads to the use of discriminant analysis in reliability engineering. However, applying the discriminant analysis techniques is very poor in the bivariate case. Here, we generalize the ratio of minimized Kullback- Leibler divergence test (RMKLD) to be used in the bivariate case.Then to illustrate this method it is applied to discriminate between the bivariate inverted Kumarswamy (BIK) and bivariate generalized exponential (BVGE) distributions

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