Statistical analysis of two-parameter generalized Birnbaum-Saunders Cauchy distribution

The image features of density function and failure rate function are studied in detail for two-parameter generalized Birnbaum-Saunders Cauchy fatigue life distribution. The logarithmic moment estimation and other two point estimations of parameters are proposed under full sample, and the precisions of point estimations are investigated by Monte-Carlo simulations. The approximate interval estimations of parameters are given by using Taylor expansion, and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations. Finally, several examples show the feasibility of the methods.     

A new generalized linear exponential distribution and its applications

A new generalized linear exponential distribution （NCLED） is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations （MLE） of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.     

离散二元几何分布串联系统的参数估计

本文首次给出了二元几何分布的定义及其主要性质,并针对二元几何分布串联系统给出了参数的矩估计和极大似然估计,同时通过大量Monte-Carlo模拟考察了估计的精度,文章最后通过Monte-Carlo数值例子来说明方法的运用.     

逐步增加的Ⅱ型截尾下系统可靠性的Bayes分析及寿命预测

在逐步增加的型截尾模型下,研究部件寿命服从双参数指数分布的冷贮备串联系统可靠性指标的Bayes估计及单样本场合未来观测值的预测问题.在两个参数均未知的情形下,分别在平方损失(SE)、LINEX损失和熵(General Entropy,GE)损失函数下给出两个参数及可靠性指标的Bayes估计,对于超参数的确定,给出一种新的方法;并讨论了单样本场合未来观测值的预测问题,给出预测分布及预测区间;最后利用随机模拟方法进行比较,并对结果进行了讨论.     

双边定数截尾下Pareto分布的可靠性分析

基于双边定数截尾样本,选取未知参数的先验分布为无信息先验和Gamma分布,分别在平方损失和LINEX损失下,研究了Pareto分布的形状参数和可靠性指标(可靠度和失效率)的Bayes估计.为了研究估计的精度,采用Monte-Carlo模拟的方法给出了数值检验的例子.结果表明在LINEX损失下并选用Gamma先验分布时,参数的Bayes估计是最优的.     

删失截断情形下失效率变点模型的Bayes参数估计

通过添加部分缺失寿命变量数据,得到了删失截断情形下失效率变点模型相对简单的似然函数.讨论了所添加缺失数据变量的概率分布和随机抽样方法.利用Monte Carlo EM算法对未知参数进行了迭代.结合Metropolis-Hastings算法对参数的满条件分布进行了Gibbs抽样,基于Gibbs样本对参数进行估计,详细介绍了MCMC方法的实施步骤.随机模拟试验的结果表明各参数Bayes估计的精度较高.     

指数分布卷积形式参数的估计

本文研究指数分布卷积形式参数的点估计，区间估计以及经验分布函数与分布函数最大偏差的概率估计．     

关于可靠性生存寿命分析中几类重要截尾分布函数参数的最佳有效无偏估计

在给出了可靠性生存寿命分析几类重要随机截尾分布函数的基础上,讨论了寿命分布函数参数的最佳有效无偏估计,为解决可靠性生存寿命分析以及通讯工程和电力负载预测中的最佳无偏误差估计问题提供了令人满意的可靠依据和有效算法．     

并联压力—强度模型可靠性研究

In this paper,the reliability of a parallel stress-strength model of exponentiated Pareto distribution is discussed.Different point estimations and interval estimations are proposed.The point estimators obtained are maximum likelihood and Bayesian estimators.The interval estimations obtained are approximate,exact,bootstrap-p and bootstrap-t confidence intervals and Bayesian credible interval.Different methods and the corresponding confidence intervals are demonstrated using some simulation studies.     

定数截尾指数分布参数的具有一致最小平均长度的区间估计

设随机变量Ｘ服从指数分布ｆ（ｘ，θ）．研究并给出了指数分布平均寿命参数和平均失效率参数的具有一致最小平均长度的区间估计，计算方法和数值用表．     

Statistical analysis of progressive stress accelerated life test for the product of two-parameter Laplace BS fatigue life distribution under inverse power law model

Based on the product of two-parameter Laplace Birnbaum-Saunders fatigue life distribution, its failure distribution mode is theoretically derived under the progressive stress accelerated life test with inverse power law model, and then three-parameter generalized Laplace Birnbaum-Saunders fatigue life distribution is introduced. The basic properties of three-parameter generalized Laplace Birnbaum-Saunders fatigue life distribution are analyzed, and the image characteristics of its density function, failure rate function and average failure rate function are investigated. Meanwhile, the point estimate method is given for three parameters, and then the point estimates of parameters are obtained for the product of two-parameter Laplace Birnbaum-Saunders fatigue life distribution under the progressive stress accelerated life test with inverse power law model. In addition, the practical example and simulation examples are illustrated to show the feasibility of the proposed method.     

指数分布冷贮备系统产品的统计分析——转换开关完全可靠的情形

本文给出了全样本场合指数分布冷贮备系统产品在转换开关完全可靠的情形下参数的矩估计、极大似然估计、精确区间估计和近似区间估计,并通过大量Monte-Carlo模拟说明估计的精度。     

逐步增加首失效截尾样本下参数估计的优良性

在对称平方损失函数下, 利用逐步增加首失效截尾样本, 研究两参数Pareto分布族参数的一致最小方差无偏估计(UMVUE), Bayes估计和参数型经验Bayes(PEB)估计. 按照均方误差(MSE)准则, 比较UMVUE与PEB估计的优良性. 根据风险函数导出Bayes估计与PEB估计的渐近性, 并获得它们的收敛速度. 在相同的置信水平下, 研究参数分别在经典统计和Bayes统计中的区间估计, 并利用数值模拟说明Bayes区间估计的精度高于经典统计区间估计.     

基于分组数据的指数分布参数的同变估计

给出了基于分组数据的指数分布参数的同变估计,其中位置参数是最优同变估计,刻度参数为近似最优同变估计,最后通过Monte-Carlo模拟数据说明方法的可行性.     

指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用

讨论三参数一般指数分布的参数估计,首先讨论了三参数一般指数分布参数的最大似然估计的求解问题,当其中参数α=1时,应用指数分布抽样基本定理,得到了三参数一般指数分布其它参数的一致最小方差无偏估计;并且由此给出求解三参数一般指数分布参数最大似然估计的迭代方法,得到了三参数一般指数分布参数最大似然估计的近似值,给出了模拟结果以说明迭代方法的收敛性;并以相关文献的观察数据作为样本,得到了三参数一般指数分布的参数估计,从而说明了迭代方法的有效性.     

Gamma分布环境因子的统计分析

证明了Gamma分布环境因子的最大似然估计是有偏估计,且其偏差为正,进而导出了Gamma分布环境因子的近似无偏估计.利用Cornish-Fisher展开导出了Gamma分布环境因子的广义置信区间,另外也给了Gamma分布环境因子的Bootstrap-t置信区间.利用模拟方法研究了所给近似无偏估计和区间估计的精度,模拟结果显示所给近似无偏估计和区间估计的精度是相当好的.     

广义指数分布下恒定应力加速寿命试验的贝叶斯分析

研究产品寿命服从广义指数分布的有关加速寿命试验的贝叶斯统计分析.首先介绍了广义指数分布在恒定应力下的加速寿命试验基本过程;其次在完全样本,和定数截尾样本下,分别给出了广义指数分布参数的贝叶斯估计;最后运用随机模拟方法对各种估计结果的优良性进行了分析比较.     

两参数指数分布产品全样本场合下步进应力加速寿命试验损伤失效率模型下的统计分析

本文给出了两参数指数分布产品全样本场合下步进应力加速寿命试验损伤失效率模型下参数的极大似然估计和拟矩估计,并通过Monte-Carlo模拟说明本文方法的可行性.     

Statistical Analysis in Constant-Stress Accelerated Life Tests for Generalized Exponential Distribution Based on Adaptive Type-II Progressive Hybrid Censored Data

Based on adaptive type-II progressive hybrid censored data statistical analysis for constant-stress accelerated life test (CS-ALT) with products' lifetime following two-parameter generalized exponential (GE) distribution is investigated. The estimates of the unknown parameters and the reliability function are obtained through a new method combining the EM algorithm and the least square method. The observed Fisher information matrix is achieved with missing information principle, and the asymptotic unbiased estimate (AUE) of the scale parameter is also obtained. Confidence intervals (CIs) for the parameters are derived using asymptotic normality of the estimators and the percentile bootstrap (Boot-p) method. Finally, Monte Carlo simulation study is carried out to investigate the precision of the point estimates and interval estimates, respectively. It is shown that the AUE of the scale parameter is better than the corresponding two-step estimation, and the Boot-p CIs are more accurate than the corresponding asymptotic CIs.     

Reliability Statistical Analysis of Two-parameter Exponential Distribution under Constant Stress Accelerated Life Test with Inverse Power Law Model

Based on the inverse power law model, the maximum likelihood estimation and interval estimation of two-parameter Exponential distribution are derived in detail under constant stress accelerated life test. Secondly, the accuracy of point estimation and interval estimation is investigated by a large number of Monte Carlo simulations. Finally, examples and simulation examples are given to illustrate the application of the proposed method.