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Abstract
The aim of this paper is to consider the bivariate inverse generalized exponential distribution which has a singular component. The bivariate inverse generalized exponential distribution can be used when the marginals have heavy tailed distributions, and they have non-monotone hazard functions. Due to presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four dimensional optimization problem. To avoid that we have proposed to use an EM algorithm and it involves solving only one non-linear equation at each ‘E’-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the model.
Acknowledgements
The authors would like to thank the reviewers and the Associate editor for their constructive comments, which have helped to improve the manuscript significantly.