基于上记录值Lomax分布的统计推断

The Statistical Inference for Lomax Distribution Based on Upper Record Values

基于上记录值,该文讨论了在Lomax分布总体中未知参数、系统可靠度及失效率的极大似然估计,并利用中心极限定理得到了模型参数的近似置信区间.首先,当2个参数的先验分布为混合分布时,在2种损失函数下计算了未知参数及可靠性指标的Bayes估计,并给出了超参数的估计方法;然后,分别用频率方法和Bayes方法对未来的上记录值进行预测;最后,提出了一种模拟上记录值的算法,利用模拟的记录值计算了相关的结果.

Based on the upper recorded values,the maximum likelihood estimates of the unknown parameters,system reliability and failure rate for Lomax distribution population are discussed.The approximate confidence intervals of the model parameters are obtained by using the central limit theorem.When the prior distributions of the two parameters are taken as a mixed distribution,the Bayesian estimates of the unknown parameters and reliability indexes are calculated under two loss functions,and the estimation approach of the hyperparameters is given.Frequentist method and Bayesian method are used to predict the future upper recorded values,respectively.Finally,the algorithm for simulating the upper record values is proposed,and the relevant results are calculated by using the simulated record values.