Abstract
In this paper, statistical inference and prediction issue of left truncated and right censored dependent competing risk data are studied. When the latent lifetime is distributed by Marshall–Olkin bivariate Rayleigh distribution, the maximum likelihood estimates of unknown parameters are established, and corresponding approximate confidence intervals are also constructed by using a Fisher information matrix and asymptotic approximate theory. Furthermore, Bayesian estimates and associated high posterior density credible intervals of unknown parameters are provided based on general flexible priors. In addition, when there is an order restriction between unknown parameters, the point and interval estimates based on classical and Bayesian frameworks are discussed too. Besides, the prediction issue of a censored sample is addressed based on both likelihood and Bayesian methods. Finally, extensive simulation studies are conducted to investigate the performance of the proposed methods, and two real-life examples are presented for illustration purposes.
Highlights
Motivated by the reasons mentioned above and due to the simplicity and practicability of the Marshall–Olkin type bivariate distribution, this paper aims to discuss the statistical inference for left truncated and right censored (LTRC) data with dependent competing risks
When the dependent causes of failure is modeled by Marshall–Olkin Rayleigh (MOBR) distribution, various estimators are provided for unknown model parameters from classical and Bayesian perspectives, and extensive simulation studies and real life examples are carried out to compare the performance of different methods.In addition, for the sake of clarity, the main motivations and contributions of our paper could be presented as follows
When the dependent competing risks is distributed by the Marshall–Olkin bivariate Rayleigh model, the maximum likelihood estimators of unknown parameters are established, and associated approximate confidence intervals are constructed
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Kundu et al [19] provided the Bayesian inference for the unknown parameters of MOBW distribution when LTRC competing risk model is available with independent causes. Motivated by the reasons mentioned above and due to the simplicity and practicability of the Marshall–Olkin type bivariate distribution, this paper aims to discuss the statistical inference for LTRC data with dependent competing risks. When the dependent causes of failure is modeled by Marshall–Olkin Rayleigh (MOBR) distribution, various estimators are provided for unknown model parameters from classical and Bayesian perspectives, and extensive simulation studies and real life examples are carried out to compare the performance of different methods.In addition, for the sake of clarity, the main motivations and contributions of our paper could be presented as follows.
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