Statistical analysis of Gompertz distribution based on progressively type-II censored competing risk model with binomial removals

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimators is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods.

本文考虑具有二项剔除（binomial removals）的竞争风险模型（competing risks model）下的渐进II型删失（progressive Type-II censoring）Gompertz数据。通过数值方法获得了所涉及模型参数的极大似然估计量（maximum likelihood estimators），并推导了估计量的渐近方差-协方差矩阵（asymptotic variance-covariance matrix）。基于重要性抽样程序（importance sampling procedure），在平方误差、LINEX及广义熵损失函数（general entropy loss functions）下，构建了贝叶斯估计（Bayesian estimates）。同时，基于渐近正态性及贝叶斯方法，构建了置信区间（confidence intervals）。最后，通过蒙特卡洛模拟（Monte Carlo simulation）评估了上述所有不同估计方法下所提估计量的性能。