左截断右删失数据下伽马分布的参数推断

Parameter inference of Gamma distribution with left truncated and right censored data

伽马分布是生存分析中应用较为广泛的一种连续型寿命分布。本文基于矩估计方法研究左截断右删失数据下伽马分布的参数估计问题,通过引入潜在数据推导出参数迭代公式,利用矩估计方法的渐近正态性质得到伽马分布参数的渐近置信区间,并进行数值模拟实验。模拟结果表明:在删失比例较小的情况下,参数推断的结果更接近真值;矩估计方法适合大样本情况,同种删失比例随着样本量增大,参数估计的效果更好,渐近置信区间长度变短。

Gamma distribution is a widely used continuous type of lifetime distribution in survival analysis.Based on the moment estimation method,the parameter estimation of gamma distribution of left truncated and right censored data is studied.The parameter iteration formula is derived by introducing potential data,and the asymptotic confidence interval of Gamma distribution parameters is obtained by using the asymptotic normality of moment estimation method.Then,numerical simulation experiments are carried out.The simulation results show that the parameter inference results are close to the true value when the deletion ratio is small.The moment estimation is suitable for large sample case.With the increase of sample size,the effect of parameter estimation is better and the asymptotic confidence interval is shorter.