定数截尾下Lomax分布失效率和可靠度的贝叶斯估计

由定数截尾寿命试验数据，得到了样本的似然函数. 当取形状参数的先验分布分别为共轭先验分布族和Jeffreys先验时，根据贝叶斯公式得到了形状参数的后验分布，并进一步得到了失效率和可靠度的后验分布.当取平方损失和熵损失函数时，根据后验风险最小的原则,由贝叶斯统计方法得到了失效率和可靠度的贝叶斯估计.通过计算机随机模拟1 000次得到失效率和可靠度的均值和均方误差，并且从均值和均方误差两方面对几个估计值进行了比较，结果表明如果没有充分的先验信息可以利用，无法得到超参数a、b较为准确的估计时，应优先使用Jeffreys先验.

Bayesian Estimation of Failure Rate and Reliability on Lomax Distribution Under Type-II Censored Samples

Likelihood function of the samples is got by type-II censored life test data. Taking the prior distribution of the shape parameter as conjugate prior distribution and Jeffreys prior distribution respectively, posterior distribution of the shape parameter is obtained according to the Bayesian formula, and further the posterior distribution of the failure rate and reliability are obtained. When choosing square loss and entropy loss function, based on the principle of minimum posterior risk, Bayesian estimation of the failure rate and reliability are obtained through the Bayesian statistical method. Mean and mean square error of the failure rate and reliability are obtained through the computer's 1000 times stochastic simulation. Several estimates are compared from two aspects of mean and mean square error. Further if there is no sufficient prior information can be used, and more accurate estimation of super parameters a, b could not be obtained, it is recommended to use Jeffreys prior.