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Ph.D. Shahid Beheshti University
Abstract:   (42 Views)

‎Many distributions have been presented with bathtub-shaped failure rates for real-life data‎. ‎A two-parameter distribution was defined by  Chen (2000)‎. ‎This distribution can have a bathtub-shaped or increasing failure rate function‎. ‎In this paper‎, ‎we consider that two bivariate models based on the proposed distribution by Chen and use the proposed methods of  Marshall and Olkin (1967) in bivariate case and  Marshall and Olkin (1997) in the univariate cases‎. ‎In the second case‎, ‎their method is generalized to bivariate case and a new bivariate distribution is introduced‎. ‎These new bivariate distributions have natural interpretations‎, ‎and they can be applied in fatal shock models or in competing risks models‎. ‎We call these new distributions as the bivariate Chen (BCH) distribution and bivariate Chen-geometric (BCHG) distribution‎, ‎respectively‎. ‎Moreover‎, ‎the BCH can be obtained as a special case of the BCHG model‎. ‎Then‎, ‎the various properties of the new distributions are investigated‎. ‎The BCHG distribution has five parameters and the maximum likelihood estimators cannot be obtained in closed form‎. ‎We suggest using an EM algorithm that is very easy to implement‎. ‎Also‎, ‎Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm‎. ‎Finally‎, ‎we analyze two real data sets for illustrative purposes‎. ‎

Type of Study: Original Paper | Subject: 62Hxx: Multivariate analysis
Received: 2017/12/18 | Accepted: 2018/07/9