On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with different methods

ABSTRACT

Competing risks models are of great importance in reliability and survival analysis. They are often assumed to have independent causes of failure in literature, which may be unreasonable. In this article, dependent causes of failure are considered by using the Marshall–Olkin bivariate Weibull distribution. After deriving some useful results for the model, we use ML, fiducial inference, and Bayesian methods to estimate the unknown model parameters with a parameter transformation. Simulation studies are carried out to assess the performances of the three methods. Compared with the maximum likelihood method, the fiducial and Bayesian methods could provide better parameter estimation.

KEYWORDS:

• Bayesian method
• Competing risks model
• Fiducial inference
• Marshall–Olkin bivariate Weibull distribution
• Maximum likelihood method

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N05
• 62N86