Sequential Analysis-Design Methods and Applications最新文献

Distribution of number of observations required to obtain a cover for the support of a uniform distribution 为支持均匀分布而获得覆盖所需的观测数的分布

4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-09-20 DOI: 10.1080/07474946.2023.2242414

R. N. Rattihalli

{"title":"Distribution of number of observations required to obtain a cover for the support of a uniform distribution","authors":"R. N. Rattihalli","doi":"10.1080/07474946.2023.2242414","DOIUrl":"https://doi.org/10.1080/07474946.2023.2242414","url":null,"abstract":"AbstractFor a given positive number ‘δ′, we consider a sequence of δ− neighborhoods of the independent and identically distributed (i.i.d.) random variables, from a U(0,1) distribution, and “stop as soon as their union contains the interval (0,1).” We call such a union “a cover.” To find the distributions of N(δ), the stopping time random variable, we need the joint distribution of order statistics from a U(0,1) distribution. For each δ>0 and n=1,2,…, we obtain a general expression for P(N(δ)≤n), and for a fixed value of δ, it is the distribution function of N(δ). For a given n, let Δ(n) be the minimum value of δ, so that the union of the n δ− neighborhoods of the first n observations contains the interval (0,1). Because N(δ)≤n if and only if Δ(n)≤δ, the distributions of Δ(n) can be obtained by fixing n in the general expression for P(N(δ)≤n). To describe the impact of δ on the distribution of N(δ) and that of n on Δ(n), we sketch the graphs of distribution functions and the empirical distribution functions.Keywords: Neighborhoodstopping ruleuniform distributionSubject Classification: MSC 2020: 26B1562E15 ACKNOWLEDGMENTThanks to S. B. Patil and S. R. Rattihalli for their computational assistance.DISCLOSUREThe author has no conflicts of interest to report.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136264741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bayesian and non-Bayesian inference for a general family of distributions based on simple step-stress life test using TRV model under type II censoring 基于TRV模型的简单阶跃应力寿命检验的一般分布族的贝叶斯和非贝叶斯推理

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-09-04 DOI: 10.1080/07474946.2023.2224401

S. Dutta, Farha Sultana, S. Kayal

引用次数: 0

A Sequential Test of Traffic Intensity for the M/M/1 Queueing System M/M/1排队系统交通强度的序列检验

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-07-03 DOI: 10.1080/07474946.2023.2204888

Murat Sagir

引用次数: 0

Two-stage estimation of the combination of location and scale parameter of the exponential distribution under the constraint of bounded risk per unit cost index 在单位成本有界风险指标约束下，结合区位和规模参数的指数分布的两阶段估计

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-07-03 DOI: 10.1080/07474946.2023.2201607

E. Mahmoudi, Zahra Nemati, Ashkan Khalifeh

引用次数: 0

Comparison of Gini indices using sequential approach: Application to the U.S. Small Business Administration data 使用顺序方法比较基尼指数:应用于美国小企业管理局的数据

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-07-03 DOI: 10.1080/07474946.2023.2193612

Francis Bilson Darku, Dorcas Ofori-Boateng, Bhargab Chattopadhyay

{"title":"Comparison of Gini indices using sequential approach: Application to the U.S. Small Business Administration data","authors":"Francis Bilson Darku, Dorcas Ofori-Boateng, Bhargab Chattopadhyay","doi":"10.1080/07474946.2023.2193612","DOIUrl":"https://doi.org/10.1080/07474946.2023.2193612","url":null,"abstract":"Abstract The comparison of Gini inequality indices is an important study related to regional imbalance in equality. In the design of such a study, both the cost constraints and variability of the difference of inequality indices play an active role. In this article, we compare the Gini inequality indices for two regions under cost constraints leveraging on the concept of sequential analysis. Without prior knowledge of the statistical distributions of the data in the two regions of interest, the optimal sample sizes that balance the cost constraint and the accuracy of the comparison cannot be calculated under a fixed-sample-size methodology. Therefore, in this article, we develop a sequential procedure for comparing Gini indices for two regions under a budget constraint. With no specific assumption about the population distribution of the data, we examine and prove the large-sample properties offered by the proposed purely sequential procedure. Further, we use extensive simulations to empirically examine the characteristics of this procedure and illustrate its application using data on the Paycheck Protection Program loan from the U.S. Small Business Administration for the states of Connecticut and Rhode Island.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44226070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An ARL-unbiased modified chart for monitoring autoregressive counts with geometric marginal distributions 一种用于监测具有几何边缘分布的自回归计数的arl无偏修正图

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-07-03 DOI: 10.1080/07474946.2023.2221996

Manuel Cabral Morais, P. Wittenberg, S. Knoth

引用次数: 0

Real-time change point detection in linear models using the ranking selection procedure 实时变化点检测在线性模型中使用排序选择程序

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-04-03 DOI: 10.1080/07474946.2023.2187416

Chao Gu, Suthakaran Ratnasingam

引用次数: 0

Group-sequential response-adaptive designs for multi-armed trials 多武器试验的群序列反应自适应设计

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-04-03 DOI: 10.1080/07474946.2023.2184831

Wenyu Liu, D. Coad

{"title":"Group-sequential response-adaptive designs for multi-armed trials","authors":"Wenyu Liu, D. Coad","doi":"10.1080/07474946.2023.2184831","DOIUrl":"https://doi.org/10.1080/07474946.2023.2184831","url":null,"abstract":"Abstract Several experimental treatments are often compared with a common control in a clinical trial nowadays. A group-sequential design incorporating response-adaptive randomization can help to increase the probability of receiving a more promising treatment for patients in the trial and to detect a treatment effect early so as to benefit the whole population of interest. With such ethical advantages, the trial design has invoked investigation using the Bayesian approach. In the frequentist approach, the type I error rate of a multi-armed trial may involve two error elements, the inflated error rates caused by multiple treatment comparisons and sequential testing. In this study, a group-sequential global test was considered. By monitoring the response-adaptive design at a continuous information time, calculation of the information time and two optimal response-adaptive sampling rules for multi-armed trials were described. Operating characteristics of the designs were investigated via simulation for censored exponential survival outcomes and using patient data sampled from a four-armed binary trial to demonstrate their practical applicability. Our results showed that, in general, the adaptive designs preserved ethical advantages in terms of reducing the average numbers of patients and failures compared with a group-sequential non-adaptive randomized design, while not adversely affecting the power.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48620301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

One-sided maximal inequalities for a randomly stopped Bessel process 随机停止贝塞尔过程的单侧极大不等式

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-04-03 DOI: 10.1080/07474946.2023.2193593

C. Makasu

引用次数: 0

Numerical solution of Kiefer-Weiss problems when sampling from continuous exponential families 连续指数族中Kiefer-Weiss问题的数值解

IF 0.8 4区数学

Sequential Analysis-Design Methods and Applications Pub Date : 2023-04-03 DOI: 10.1080/07474946.2023.2193602

A. Novikov, Andrei Novikov, Fahil Farkhshatov

{"title":"Numerical solution of Kiefer-Weiss problems when sampling from continuous exponential families","authors":"A. Novikov, Andrei Novikov, Fahil Farkhshatov","doi":"10.1080/07474946.2023.2193602","DOIUrl":"https://doi.org/10.1080/07474946.2023.2193602","url":null,"abstract":"Abstract In this article, we deal with problems of testing hypotheses in the framework of sequential statistical analysis. The main concern is the optimal design and performance evaluation of sampling plans in Kiefer-Weiss problems. The main goal of the Kiefer-Weiss problem is designing hypothesis tests that minimize the maximum average sample number, over all parameter values, as opposed to both the sequential probability tests (SPRTs) minimizing the average sample number only at two hypothesis points and the classical fixed-sample-size test. For observations that follow a distribution from an exponential family of the continuous type, we provide algorithms for optimal design in the modified Kiefer-Weiss problem and obtain formulas for evaluating the performance of sequential tests by calculating the operating characteristic function, the average sample number, and some related characteristics. These formulas cover, as a particular case, the SPRTs and their truncated versions, as well as optimal finite-horizon sequential tests. In the setting of the original Kiefer-Weiss problem we apply the method of our recent work (Sequential Analysis 2022, 41(2), 198–219) for numerical construction of the optimal tests. For the particular case of sampling from a normal distribution with a known variance, we make numerical comparisons of the Kiefer-Weiss solution with the SPRT and the fixed-sample-size test provided that the three tests have the same levels of the error probabilities. All of the algorithms are implemented in the form of computer code written in the R programming language and are available at the GitHub public repository (https://github.com/tosinabase/Kiefer-Weiss). Guidelines on the adaptation of the program code to other exponential family distributions are provided.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41343230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0