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Bayesian Estimation for the Two Log-Logistic Models Under Joint Type II Censoring Schemes 联合II型筛选方案下两个对数- logistic模型的贝叶斯估计
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-04-20 DOI: 10.13052/jrss0974-8024.15110
Ranjita Pandey, Pulkit Srivastava
The present paper, discusses classical and Bayesian estimation of unknown combined parameters of two different log-logistic models with common shape parameters and different scale parameters under a new type of censoring scheme known as joint type II censoring scheme. Maximum likelihood estimators are derived. Bayes estimates of parameters are proposed under different loss functions. Classical asymptotic confidence intervals along with the Bayesian credible intervals and Highest Posterior Density region are also constructed. Markov Chain Monte Carlo approximation method is used for simulating the theoretic results. Comparative assessment of the classical and the Bayes results are illustrated through a real archived dataset.
本文讨论了两种具有相同形状参数和不同尺度参数的不同逻辑-逻辑模型在一种新型的联合II型滤波方案下未知组合参数的经典估计和贝叶斯估计。得到了极大似然估计量。给出了不同损失函数下参数的贝叶斯估计。构造了经典渐近置信区间、贝叶斯可信区间和最高后验密度区域。采用马尔可夫链蒙特卡罗近似法对理论结果进行了模拟。通过一个真实的存档数据集说明了经典和贝叶斯结果的比较评估。
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引用次数: 0
On Some Improved Classes of Estimators Under Stratified Sampling Using Attribute 基于属性的分层抽样下几种改进的估计量
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-04-16 DOI: 10.13052/jrss0974-8024.1518
Shashi Bhushan, Anoop Kumar, Dushyant Tyagi, Saurabh Singh
This article establishes some improved classes of difference and ratio type estimators of population mean of study variable using information on auxiliary attribute under stratified simple random sampling. The usual mean estimator, classical ratio estimator, classical product estimator and classical regression estimator are identified as particular cases of the proposed classes of estimators for different values of the characterising scalars. The expression of mean square error of the suggested classes of estimators has been studied up to first order of approximation and their effective performances are likened with respect to the conventional as well as lately existing estimators. Subsequently, an empirical study has been carried out using a real data set in support of theoretical results. The empirical results justify the proposition of the proposed classes of estimators in terms of percent relative efficiency over all discussed work till date. Suitable suggestions are forwarded to the survey practitioners.
本文在分层简单随机抽样条件下,利用辅助属性信息建立了研究变量总体均值的差分型和比值型估计量的改进类。通常的均值估计量、经典比率估计量、古典乘积估计量和经典回归估计量被确定为针对表征标量的不同值的所提出的估计类的特定情况。研究了所提出的一类估计量的均方误差的一阶近似表达式,并将其有效性能与传统估计量和新近存在的估计量进行了比较。随后,使用真实数据集进行了实证研究,以支持理论结果。经验结果证明了所提出的估计类在迄今为止所有讨论工作的相对效率百分比方面的命题。适当的建议已转交给调查从业人员。
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引用次数: 4
Design of Fuzzy Economic Order Quantity (EOQ) Model in the Presence of Inspection Errors in Single Sampling Plans 单抽样方案存在检验误差时的模糊经济订货量(EOQ)模型设计
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-04-16 DOI: 10.13052/jrss0974-8024.1519
Julia T. Thomas, Mahesh Kumar
Inventory management is the core of the supply chain management system, in which the economic order quantity (EOQ) model is a fundamental inventory model. This paper develops a fuzzy EOQ model in the presence of inspection errors in single sampling plans. The model assumes probability of mis-classifications. An inventory system is hypothesized where the orders undergo acceptance sampling, back-orders are eliminated, and defectives are set aside from the inventory. Due to the presence of vagueness in real time data, the rate at which an order turn to be scrap, the costs of holding, and the back-orders are characterized by fuzzy random variables. Since total profit involved is a random variable, maximum total expected profit is obtained. Some numerical examples are presented, and a sensitivity analysis study is carried out to check the validity of the model developed.
库存管理是供应链管理系统的核心,其中经济订货量(EOQ)模型是一个基本的库存模型。本文建立了单个抽样方案存在检测误差时的模糊EOQ模型。该模型假设错误分类的概率。假设一个库存系统,其中订单经过验收抽样,延迟订单被消除,并从库存中排除缺陷。由于实时数据存在模糊性,订单的报废率、保持成本和未完成订单都用模糊随机变量来表征。由于所涉及的总利润是一个随机变量,因此得到最大的总期望利润。给出了一些数值算例,并进行了灵敏度分析研究,以验证所建立模型的有效性。
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引用次数: 4
Classical and the Bayesian estimation of process capability index Cpy: A comparative study 过程能力指数Cpy的经典估计与贝叶斯估计的比较研究
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-03-21 DOI: 10.13052/jrss0974-8024.1517
Sumit Kumar
In this study, to estimate the process capability index Cpy when the process follows different distributions (Lindley, Xgamma, and Akash distribution), we have used five methods of estimation, namely, the maximum likelihood method of estimation, least and weighted least squares method of estimation, maximum product of spacings method of estimation and Bayesian method of estimation. The Bayesian estimation is studied for symmetric loss function with the help of the Metropolis-Hastings algorithm method. The confidence intervals for the index Cpy are constructed based on four bootstrap methods and Bayesian methods. We studied the performances of these estimators based on their corresponding MSEs/risks for the point estimates of Cpy, and average widths AW for interval estimates. To assess the accuracy of the various approaches, Monte Carlo simulations are conducted. It is found that the Bayes estimates performed better than the considered classical estimates in terms of their corresponding risks. To illustrate the performance of the proposed methods, two real data sets are analyzed.
在本研究中,为了估计过程遵循不同分布(Lindley、Xgamma和Akash分布)时的过程能力指数Cpy,我们使用了五种估计方法,即估计的最大似然法、估计的最小和加权最小二乘法、估计的最大间隔积法和估计的贝叶斯法。利用Metropolis-Hastings算法研究了对称损失函数的贝叶斯估计。基于四种bootstrap方法和贝叶斯方法构造了指数Cpy的置信区间。我们根据Cpy点估计的MSEs/风险和区间估计的平均宽度AW来研究这些估计器的性能。为了评估各种方法的准确性,进行了蒙特卡洛模拟。研究发现,贝叶斯估计在相应的风险方面比考虑的经典估计表现得更好。为了说明所提方法的性能,对两个真实数据集进行了分析。
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引用次数: 0
A Generalized Class of Estimators for Finite Population Mean Using Two Auxiliary Variables in Sample Surveys 样本调查中使用两个辅助变量的有限总体均值的广义估计
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-02-22 DOI: 10.13052/jrss0974-8024.1514
H. P. Singh, P. Nigam
In this paper we have suggested a generalized class of estimators for estimating the finite population mean Y¯Y¯ of the study variable y using information on two auxiliary variables x and z. We have studied the properties of the proposed generalized class of estimators in simple random sampling without replacement scheme and in stratified random sampling up to the first order of approximation. It is shown that the suggested class of estimators is more efficient than the conventional unbiased estimator, ratio estimator, product estimator, traditional difference estimator, Srivastava (1967) estimator, Ray et al. (1979) estimator, Vos (1980) estimator, Upadhyaya et al. (1985) estimator, Rao (1991) estimator and Gupta and Shabbir (2008) estimator. Theoretical results are well supported through an empirical study.
本文提出了利用两个辅助变量x和z的信息估计研究变量Y的有限总体均值Y¯Y¯的广义估计量。我们研究了所提出的广义估计量在无替换方案的简单随机抽样和一阶逼近的分层随机抽样中的性质。结果表明,所建议的估计量比传统的无偏估计量、比率估计量、乘积估计量、传统的差分估计量、Srivastava(1967)估计量、Ray等人(1979)估计量、Vos(1980)估计量、Upadhyaya等人(1985)估计量、Rao(1991)估计量和Gupta和Shabbir(2008)估计量更有效。通过实证研究,理论结果得到了很好的支持。
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引用次数: 3
Predictive Modelling: An Assessment Through Validation Techniques 预测建模:通过验证技术的评估
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-02-14 DOI: 10.13052/jrss0974-8024.1513
M. Jeelani, F. Danish, Saquib Khan
In this investigation, various statistical models were fitted on simulated symmetric and asymmetric data. Fitting of models was carried out with the help of various libraries in R studio, and various selection criteria were also used while fitting of models. In order to evaluate different validation techniques the simulated data was divided in training and testing data set and various functions in R were developed for the purpose of validation. Coefficient summary revealed that all statistical models were statistically significant across both symmetric as well as asymmetric distributions. In preliminary analysis TFEM (Type First Exponential Model) was found out to be the best linear model across both symmetric and asymmetric distributions with lower values of RMSE, MAE, BIAS, AIC and BIC. Among non-linear models, Haung model was found out to be best model across both the distributions as it has lower values of RMSE, MAE etc. Different validation techniques were used in the present study. Lower rates of prediction error in comparison to its counter parts, 5-folded cross validation performed better across all the statistical models.
在本研究中,对模拟对称和非对称数据进行了各种统计模型的拟合。模型的拟合是借助R studio中的各种库进行的,模型的拟合也使用了各种选择标准。为了评估不同的验证技术,将模拟数据分为训练数据集和测试数据集,并在R中开发了各种用于验证的函数。系数总结显示,所有统计模型在对称分布和非对称分布中都具有统计学显著性。初步分析发现,在对称分布和非对称分布中,TFEM (Type First Exponential Model)是最佳的线性模型,RMSE、MAE、BIAS、AIC和BIC值都较低。在非线性模型中,Haung模型具有较低的RMSE、MAE等值,是两种分布下的最佳模型。在本研究中使用了不同的验证技术。预测错误率较低,5折交叉验证在所有统计模型中表现更好。
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引用次数: 0
Uncovering Regional Disparities in Infrastructural Development of Uttar Pradesh: An Exploratory Factor Analysis 揭示北方邦基础设施发展的区域差异:探索性因素分析
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-02-04 DOI: 10.13052/jrss0974-8024.1512
M. Dube, Subhash Kr. Yadav, Vishwajeet P. Singh
In developmental studies, the infrastructural sector is considered as an important component of overall economic development. The infrastructural growth in the state of Uttar Pradesh is undoubtedly critical since independence. The main focus of this paper is to uncover the principal factors or dimensions of infrastructural characteristics and to quantify the level of infrastructural development of Uttar Pradesh into five clusters having different grade of development using Exploratory Factor Analysis & K-means Cluster Analysis. The analysis has been carried out by taking into account various infrastructural indicators for the time period of two years from 2018 to 2019. The results of the present analysis led to the identification of the five factors of infrastructural characteristics, and the classification of all the seventy-five districts of Uttar Pradesh into five regions with different degree of infrastructural development. The ‘infrastructural regions’ uncovered through this procedure allow a much more useful characterization of Uttar Pradesh for the policy making purpose. The same technique may be applied to the whole country and other countries as well.
在发展研究中,基础设施部门被认为是全面经济发展的一个重要组成部分。自独立以来,北方邦的基础设施建设无疑是至关重要的。本文的主要重点是揭示基础设施特征的主要因素或维度,并利用探索性因子分析和k均值聚类分析将北方邦的基础设施发展水平量化为五个具有不同发展等级的集群。该分析是在考虑了2018年至2019年两年期间的各种基础设施指标后进行的。本文的分析结果确定了基础设施特征的五个因素,并将北方邦的75个区划分为基础设施发展程度不同的五个区域。通过这一过程发现的“基础设施区域”可以为制定政策提供更有用的北方邦特征。同样的技术可以应用于整个国家,也可以应用于其他国家。
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引用次数: 1
A Family of Estimators for Population Mean Under Model Approach in Presence of Non-Response 无响应情况下模型方法下总体均值的一类估计
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2022-02-04 DOI: 10.13052/jrss0974-8024.1511
A. Singh, V. K. Singh
We have defined a class of estimators for population mean under non-response error based upon the concept of sub-sampling of non-respondents utilizing an auxiliary variable. The class is a one-parameter class of estimators which is based on the idea of exponential type estimators (ETE). The model biasness and model-mean square error of the class and some of its important members have been derived under polynomial regression model (PRM). The effect of variations in PRM specifications on the efficiency of the estimators has been discussed based upon the empirical results.
基于利用辅助变量对非应答者进行亚抽样的概念,我们定义了一类非应答误差下总体均值的估计量。该类是一类基于指数型估计量思想的单参数估计量。在多项式回归模型(PRM)下,导出了该类及其一些重要成员的模型偏差和模型均方误差。基于经验结果,讨论了PRM规范的变化对估计器效率的影响。
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引用次数: 1
Reliability Test Plan Based on Logistic-Exponential Distribution and Its Application 基于Logistic指数分布的可靠性测试计划及其应用
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2021-12-14 DOI: 10.13052/10.13052/jrss0974-8024.14215
A. Yadav, Mahendra Saha, Shivanshi Shukla, Harsh Tripathi, Rajashree Dey
In this article, a reliability test plan is developed for Logistic-exponential distribution (LoED) under time truncated life test scheme. The distribution has been chosen because it can used to model lifetime of several reliability phenomenon and it performs better than many well known existing distributions. With the discussions of statistical properties of the aforesaid model, the reliability test plan has been established under the assumption of median quality characteristics when minimum confidence level P* is given. To quench the objective of the paper i.e; to serve as a guiding aid to the emerging practitioners, minimum sample sizes have been obtained by using binomial approximation and Poisson approximation for the proposed plan. Further, operating characteristic (OC) values for the various choices of quality level are placed. Also, minimum ratio of true median life to specified life has been presented for specified producer’s risk. Important findings of the proposed reliability test plan are given for considered value of k=0.75,1,2. To demonstrate the appropriateness of suggested reliability test plan is achieved using four real life situation.
提出了一种时间截断寿命试验方案下的logistic指数分布可靠性试验方案。选择该分布是因为它可以用来对几种可靠性现象的寿命进行建模,并且它比许多已知的现有分布性能更好。通过对上述模型统计特性的讨论,在给出最小置信水平P*的条件下,建立了中位数质量特征假设下的可靠性检验方案。为了达到论文的目的,即;为了给新兴的实践者提供指导,我们使用二项近似和泊松近似获得了最小样本量。此外,还列出了各种质量水平选择的操作特性(OC)值。同时,给出了特定生产者风险下的真实中值寿命与指定寿命的最小比值。考虑k=0.75,1,2时,给出了所提出的信度试验方案的重要结果。通过四种实际情况验证了所提出的可靠性试验方案的适用性。
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引用次数: 2
Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring 倒Topp-Leone分布:对存在随机滤波的j形频率函数族的贡献
IF 0.8 Q3 STATISTICS & PROBABILITY Pub Date : 2021-12-06 DOI: 10.13052/10.13052/jrss0974-8024.14212
H. Muhammed, E. A. Muhammed
In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.
本文研究了样本完全随机截尾情况下倒Topp-Leone分布形状参数的贝叶斯和非贝叶斯估计。提出了未知参数的最大似然估计量和贝叶斯估计量。贝叶斯估计(BEs)是基于平方误差损失(SEL)函数并使用马尔可夫链蒙特卡罗(MCMC)技术计算的。计算了渐近、bootstrap(p,t)和最高后验密度区间。针对贝叶斯估计,提出了Metropolis Hasting算法。进行蒙特卡罗模拟以比较所提出的方法的性能,并分析了一个真实数据集以便于说明。
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引用次数: 1
期刊
Journal of Reliability and Statistical Studies
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