混合截尾数据下艾拉姆咖分布参数的后验分布研究

Study on the Posterior Distribution of Erlang-K Parameters under Mixed Censored Data

摘要: 利用混合截尾方法，得到艾拉姆咖分布参数在无信息Jeffreys先验分布和有信息共轭先验分布下的后验分布结果的具体表达式，同时利用优化理论，给出以基本线性组合与加权线性组合下的参数的均方表达式，并利用MCMC原理，对优化结果进行数值模拟，验证优化结果的准确性与真值拟合度；针对混合截尾方法，以参数的极大似然估计结果初步确定截尾数的取值区间，同时在给定两类先验分布条件下，利用随机模拟得到不同参数条件下的后验分布初始值与优化值的散点分布图，并根据分布图确定截尾数的具体取值。

Abstract: Using the hybrid truncation method, the specific expressions of the posterior distribution results of the Erlang-K distribution parameters under non-informative prior distribution and informative conjugate prior distribution are obtained. At the same time, using optimization theory, the mean squared expressions of parameters under basic linear combination and weighted linear combination are given. Additionally, based on MCMC principles, numerical simulation of the optimization results is conducted to verify the accuracy of the optimization results and the fit to the true values. For the hybrid truncation method, the range of truncation numbers is preliminarily determined using the maximum likelihood estimation results of the parameters. Simultaneously, under the conditions of two types of given prior distributions, stochastic simulation is used to obtain scatter plots of the initial and optimized values of the posterior distribution under different parameter conditions, and the specific values of truncation numbers are determined according to the distribution plots.