记录值样本下具有``浴盆''型失效率寿命分布的最优置信集估计
Optimal Estimation of Confidence Set for a Bathtub-Shaped Lifetime Distribution under Records
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摘要: 本文针对具有一种具有``浴盆''型失效率曲线的寿命分布, 在记录值样本下研究模型参数的置信集估计问题. 通过构造枢轴量,首先建立了模型参数的精确置信区间和置信域. 进一步, 在给定显著性水平下,利用拉格朗日乘子法, 构造了模型参数的最优置信区间和最优置信域估计. 最后,通过算例分析研究了结果的优良性.Abstract: In this paper, confidence set estimation is considered for the parameters from a bathtub-shaped lifetime distribution when record value is available. Based on proposed pivotal quantities, exact confidence intervals and confidence regions are established firstly for the model parameters. In addition, the corresponding optimal confidence intervals and confidence regions are also constructed by using Lagrange multiplier method under given significance level. Finally, simulation studies and a real life example are provided for illustration.