On a class exhibiting trend change in average failure rate

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984 Loh, W. Y. 1984. A new generalization of the class of NBU distributions. IEEE Transactions on Reliability R-33 :97–113[Crossref], [Web of Science ®] , [Google Scholar])). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.     

Confidence intervals,significance values,maximum likelihood estimates,etc. sharpened into Occam’s razors

Abstract

Confidence sets, p values, maximum likelihood estimates, and other results of non-Bayesian statistical methods may be adjusted to favor sampling distributions that are simple compared to others in the parametric family. The adjustments are derived from a prior likelihood function previously used to adjust posterior distributions.     

The Optimal Allocation Combination for the One-Sided Sequential Screening Procedure Based on the Individual Misclassification Error

In this article, the expected total costs of three kinds of quality cost functions for the one-sided sequential screening procedure based on the individual misclassification error are obtained, where the expected total cost is the sum of the expected cost of inspection, the expected cost of rejection, and the expected cost of quality. The computational formulas for three kinds of expected total costs are derived when k screening variables are allocated into r stages. The optimal allocation combination is determined based on the criterion of minimum expected total cost. At last, we give one example to illustrate the selection of the optimal allocation combination for the sequential screening procedure.     

Estimating E-bayesian and hierarchical bayesian of scalar parameter of gompertz distribution under type II censoring schemes based on fuzzy data

In this study, the E-Bayesian and hierarchical Bayesian of the scalar parameter of a Gompertz distribution under Type II censoring schemes were estimated based on fuzzy data under the squared error (SE) loss function and the efficiency of the proposed methods was compared with each other and with the Bayesian estimator using Monte Carlo simulation.     

Slashed power-Lindley distribution

In this article, we introduce the slashed power-Lindley distribution. This model can be seen as an extension of the power-Lindley distribution with more flexibility in terms of the kurtosis of distribution. It arises as the ratio of two independent random variables, the one being a power-Lindley distribution and a power of the uniform distribution. We present properties and carry out estimates of the model parameters by the maximum likelihood method. Finally, we conduct a small simulation study to evaluate the performance of maximum likelihood estimators and we analyze a real data set to illustrate the usefulness of the new model.     

The quantile-based flattened logistic distribution: Some properties and applications

In this paper, the quantile-based flattened logistic distribution has been studied. Some classical and quantile-based properties of the distribution have been obtained. Closed form expressions of L-moments, L-moment ratios and expectation of order statistics of the distribution have been obtained. A quantile-based analysis concerning the method of matching L-moments estimation is employed to estimate the parameters of the proposed model. We further derive the asymptotic variance–covariance matrix of the matching L-Moments estimators of the proposed model. Finally, we apply the proposed model to simulated as well as two real life datasets and compare the fit with the logistic distribution.     

Predictive Inference and Scientific Reproducibility

ABSTRACT

Most statistical analyses use hypothesis tests or estimation about parameters to form inferential conclusions. I think this is noble, but misguided. The point of view expressed here is that observables are fundamental, and that the goal of statistical modeling should be to predict future observations, given the current data and other relevant information. Further, the prediction of future observables provides multiple advantages to practicing scientists, and to science in general. These include an interpretable numerical summary of a quantity of direct interest to current and future researchers, a calibrated prediction of what’s likely to happen in future experiments, a prediction that can be either “corroborated” or “refuted” through experimentation, and avoidance of inference about parameters; quantities that exists only as convenient indices of hypothetical distributions. Finally, the predictive probability of a future observable can be used as a standard for communicating the reliability of the current work, regardless of whether confirmatory experiments are conducted. Adoption of this paradigm would improve our rigor for scientific accuracy and reproducibility by shifting our focus from “finding differences” among hypothetical parameters to predicting observable events based on our current scientific understanding.     

需求分布规律变化情况下的报童订货策略

在需求分布规律变化情况下，报童在进行订货决策时会因为错误判断需求分布规律而导致期望库存成本增加。为了解决这一问题，本文集成传统历史需求信息和非传统需求信息以正确地认知需求分布规律，在此基础上决策订货量。假设需求服从均值不同、方差相同的两种类型的正态分布，每一种正态分布的概率已知。利用信号检测理论构建基于历史需求信息与需求分布概率的报童最优订货策略，并与只基于需求分布概率的直觉规则订货策略进行对比。结果表明：只要排除需求分布概率很大或很小两种极端情况，最优订货策略比直觉规则订货策略在控制期望库存成本方面的作用更明显，即利用历史需求信息可以有效修正报童对实际需求分布的检测结果，从而提高实际订货决策的准确性。研究结果对传统历史需求信息和非传统需求信息的集成以及需求信息交换等有一定的管理学启示和应用价值。     

数据驱动下收货方质量偏好与电商配送服务质量优化

针对"互联网+大数据"优化电商配送服务质量问题，明确不同收货方的质量需求稳定性，引导电商根据收货方不同质量敏感性提供相对精准服务，提升配送服务质量。模拟投票结果的形成过程聚类得到收货方对服务质量偏好的记忆性特征：（1）"无记忆"型收货方；（2）"记忆"型收货方；（3）"不确定"型收货方；（4）收货方总体。进一步推导不同规划类型求解空间，设计得到"无记忆"型收货方动态规划精确求解方法，及其他三种类型近似求解粒子群算法。研究过程中，配送资源质量感知度被嵌入到模型约束；"无记忆"型收货方的质量需求规划问题转化为零库存策略最优解问题，进而证明存在精确解；"记忆"型收货方呈现出对质量感知的累积；"不确定"型收货方模型通过赋值即可得总体收货方表达式。结果表明：数据驱动研究框架借助大数据资源，使得电商更易通过收货方的质量偏好设计更加匹配的配送方案；不确定服务需求得到有效满足，投入成本的利用率更高；通过特征分类的方式，尽可能地抽取能够精确最优化的部分，缩小NP范围，提高整体求解的精确度。