左删失恒定应力部分加速寿命试验下逆Rayleigh分布的参数估计

在恒定应力部分加速寿命试验下，基于左删失样本,研究了逆Rayleigh分布的参数估计问题。运用极大似然法得到未知参数和加速因子的极大似然估计。根据Louis提出的缺失信息原则,计算了Fisher信息矩阵，得到分布参数和加速因子的近似置信区间。当取参数的先验分布为指数分布时，在平方损失函数下求得了参数的贝叶斯估计，并利用极大似然法估计了超参数。通过 Monte Carlo 模拟，得到估计量的均方误差，据此对极大似然估计和贝叶斯估计进行了比较。最后，计算了不同左删失样本下逆Rayleigh分布参数及加速因子的估计。

Parameter estimation of inverse Rayleigh distribution for constant-stress partially accelerated life tests with left censoring

In the constant-stress partial accelerated life test, estimation of the parameter for inverse Rayleigh distribution is studied based on left censored samples. Maximum likelihood method is used to obtain the maximum likelihood estimations of the unknown parameter and acceleration factor. The Fisher information matrix is calculated according to the principle of missing information proposed by Louis, meanwhile the approximate confidence intervals of the distributed parameter and the acceleration factor are obtained. When the prior distributions of the parameters are exponential distribution, the Bayesian estimations of the parameters are obtained under the square loss function, and the maximum likelihood method is used to get the estimations of the super parameters. The mean square errors of the estimators are calculated by Monte Carlo simulation, based on these, the maximum likelihood estimation and Bayesian estimation are compared. Finally, the parameter of the inverse Rayleigh distribution and the estimation of acceleration factor are calculated for different left censored samples.