Statistical Analysis of Bivariate Failure Time Data Based on Bathtub-Shaped Failure Rate Model

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Shoaee Shirin

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Journal Paper

Paper Information

Journal: JOURNAL OF THE IRANIAN STATISTICAL SOCIETY Year:2019 | Volume:18 | Issue:1 Page(s): 53-87

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Title

Statistical Analysis of Bivariate Failure Time Data Based on Bathtub-Shaped Failure Rate Model

Author(s)

Shoaee Shirin | Issue Writer Certificate

Keywords

Bathtub-Shaped failure rate

Bivariate model

EM algorithm

Monte Carlo simulation

Pseudo likelihood function

Abstract

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 two bivariate models based on the proposed distribution by Chen and use the proposed methods of Marshall and Olkin (1967) in the bivariate case and Marshall and Olkin (1997) in the univariate case. In the second case, their method is generalized to the 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 a 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.

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APA: Copy

Shoaee, Shirin. (2019). Statistical Analysis of Bivariate Failure Time Data Based on Bathtub-Shaped Failure Rate Model. JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS), 18(1), 53-87. SID. https://sid.ir/paper/730402/en

Vancouver: Copy

Shoaee Shirin. Statistical Analysis of Bivariate Failure Time Data Based on Bathtub-Shaped Failure Rate Model. JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS)[Internet]. 2019;18(1):53-87. Available from: https://sid.ir/paper/730402/en

IEEE: Copy

Shirin Shoaee, “Statistical Analysis of Bivariate Failure Time Data Based on Bathtub-Shaped Failure Rate Model,” JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS), vol. 18, no. 1, pp. 53–87, 2019, [Online]. Available: https://sid.ir/paper/730402/en

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