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

作　　者：王亮 左烜嘉 马金歌 WANG Liang;ZUO Xuanjia;MA Jin'ge(School of Mathematics,Yunnan Normal University,Kunming,650500,China;School of Mathematics and Statistics,Xidian University,Xi'an,710071,China)

机构地区：[1]云南师范大学数学学院,昆明650500 [2]西安电子科技大学数学与统计学院,西安710071

出　　处：《应用概率统计》2022年第6期825-835,共11页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:12061091);云南省科技计划基础研究面上项目(批准号:202101AT070103);中国博士后基金项目(批准号:2019M650260)资助。

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.In this paper,confidence set estimation is considered for the parameters from a bathtubshaped 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.

关 键 词：浴盆型寿命分布 记录值样本 枢轴量 最优置信集 拉格朗日乘子法 

分 类 号：O212.1[理学—概率论与数理统计]