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Generalization of the Ratio of Minimized Kullback- Leibler Divergence Discrimination Technique to Bivariate Marshall-Olkin Family |
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PP: 57-73 |
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doi:10.18576/jsap/110105
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Author(s) |
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Hanan. M. Aly,
Ola. A. Abuelamayem,
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Abstract |
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| Different bivariate lifetime distributions are used to analyze lifetime data and study the reliability of the products. Sometimes, we find more than one distribution that fit the data well. In this case, we should select the best one. That is why the discriminant analysis is used. In literature, there is only one method used for bivariate lifetime distributions, which is the likelihood ratio test. In this paper, we try to generalize the ratio of minimized Kullback-Leibler divergence to be used as a discrimination method in the bivariate case and it could be applied on the bivariate Marsall-Olkin family. we will select two lifetime distributions which belong to the bivariate Marshall-Olkin family. The distributions are, bivariate generalized exponential distribution and a recently proposed distribution which is the bivariate inverted Kumaraswamy distribution. We compared the proposed method with likelihood ratio test after deriving its asymptotic distribution. The minimum sample size required for discrimination is obtained using the derived asymptotic distribution. A simulation study is performed to illustrate the results and it is found that ratio of minimized Kullback-Leibler divergence method performs better than likelihood ratio test method. Finally, A real dataset is analyzed.
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