Inference for dependent competing risks from bivariate Kumaraswamy distribution under generalized progressive hybrid censoring

Abstract

In this paper, competing risks model is considered when causes of failure are dependent. When latent failure times are distributed by the Marshall-Olkin bivariate Kumaraswamy model, inference for the unknown model parameters is studied under a generalized progressive hybrid censoring. Maximum likelihood estimates of unknown parameters are established, and the associated existence and uniqueness are provided. The approximate confidence intervals are constructed via the observed Fisher information matrix. Moreover, Bayes estimates and the credible intervals of the unknown parameters are also presented based a flexible Gamma-Dirichlet prior, and the importance sampling method is used to compute associated estimates. Simulation study and a lifetime example are given for illustration purposes.

Keywords:

• Dependent competing risks
• Generalized progressive hybrid censoring
• Bivariate Kumaraswamy distribution
• Maximum likelihood estimation
• Posterior analysis
• Monte-Carlo Simulation

Mathematics Subject Classification:

• 62F10
• 62F15

Acknowledgments

The authors wish to thank the Editor and referees for their valuable suggestions which led to the improvement of this paper.

Additional information

Funding

This work of Liang Wang is supported by the China Postdoctoral Science Foundation (No. 2019M650260), the National Natural Science Foundation of China (Nos. 11501433, 71571144, 71401134), and the Humanities and Social Science Fund in Ministry of Education in China (18YJC910009), and the Fundamental Research Funds for the Central Universities (No. JB150717). The work of Yogesh Mani Tripathi is partially supported under a grant EMR/2016/001401 SERB, India.