Competing risks model is considered with dependence causes of failure in this paper. When the latent failure times are distributed by a bivariate Gompertz model, statistical inference for the unknown model parameters is studied from classical and Bayesian approaches, respectively. Under a generalized progressive hybrid censoring, maximum likelihood estimators of the unknown parameters together with the associated existence and uniqueness are established, and the approximate confidence intervals are also obtained based on asymptotic likelihood theory via the observed Fisher information matrix. Moreover, Bayes estimates and the highest posterior density credible intervals of the unknown parameters are also provided based on a flexible Gamma–Dirichlet prior, and Monte Carlo sampling method is also derived to compute associated estimates. Finally, simulation studies and a real‐life example are given for illustration purposes.

中文翻译：

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广义渐进混合检查下双变量Gompertz分布的依赖竞争风险与部分观察到的失效原因的推断

考虑竞争风险模型与失败的成因。当潜在故障时间由双变量Gompertz模型分布时，分别从经典方法和贝叶斯方法研究未知模型参数的统计推断。在广义渐进混合检查下，建立未知参数的最大似然估计以及相关的存在性和唯一性，并且基于渐近似然理论，通过观测的Fisher信息矩阵获得近似置信区间。此外，还基于灵活的Gamma–Dirichlet先验值提供了贝叶斯估计值和未知参数的最高后验密度可信区间，并且还推导了蒙特卡洛采样方法来计算相关估计值。最后，