Abstract This article is a comparative study between the parametric asymptotic lower confidence limits and bootstrap lower confidence limits for the basic quantile based process capability indices based on the unified super-structure C N p ( u , v ) {C_{N_{p}}(u,v)} when the distribution of the quality characteristic follows an asymmetric non-normal distribution. We illustrate this method when the distribution of the quality characteristic is a member of the family of Esscher-transformed Laplace models introduced by S. George and D. George [11]. We obtain the bias corrected and accelerated (BCa) bootstrap confidence intervals of C N p ( u , v ) {C_{N_{p}}(u,v)} , which provide lower confidence intervals with coverage probability nearer to the nominal value compared to the asymptotic confidence intervals. We conclude that for asymmetric and peaked processes, the BCa confidence interval is a better alternative compared to the usual confidence intervals under the assumption that the quality characteristic follows a Gaussian type distribution. Numerical examples are given based on some real data.
摘要本文比较研究了基于统一超结构C N p _ (u,v) {C_{N_{p}}(u,v)}的质量特性服从非对称非正态分布时，基于基本分位数的过程能力指标的参数渐近置信下限与自举置信下限。当质量特征的分布是S. George和D. George[11]引入的esscher变换拉普拉斯模型族的成员时，我们说明了这种方法。我们得到了C N p _ (u,v) {C_{N_{p}}(u,v)}的偏差校正和加速(BCa)自助置信区间，与渐近置信区间相比，它提供了更低的置信区间，覆盖概率更接近标称值。我们得出结论，对于非对称和峰值过程，在质量特征遵循高斯型分布的假设下，与通常的置信区间相比，BCa置信区间是更好的选择。根据实际数据给出了数值算例。
{"title":"Bootstrap Lower Confidence Limits of Superstructure Process Capability Indices for Esscher-Transformed Laplace Distribution","authors":"Sebastian George, Ajitha Sasi","doi":"10.1515/eqc-2017-0010","DOIUrl":"https://doi.org/10.1515/eqc-2017-0010","url":null,"abstract":"Abstract This article is a comparative study between the parametric asymptotic lower confidence limits and bootstrap lower confidence limits for the basic quantile based process capability indices based on the unified super-structure C N p ( u , v ) {C_{N_{p}}(u,v)} when the distribution of the quality characteristic follows an asymmetric non-normal distribution. We illustrate this method when the distribution of the quality characteristic is a member of the family of Esscher-transformed Laplace models introduced by S. George and D. George [11]. We obtain the bias corrected and accelerated (BCa) bootstrap confidence intervals of C N p ( u , v ) {C_{N_{p}}(u,v)} , which provide lower confidence intervals with coverage probability nearer to the nominal value compared to the asymptotic confidence intervals. We conclude that for asymmetric and peaked processes, the BCa confidence interval is a better alternative compared to the usual confidence intervals under the assumption that the quality characteristic follows a Gaussian type distribution. Numerical examples are given based on some real data.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"71 1","pages":"87 - 98"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86611477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.
{"title":"The Exponentiated Generalized-G Poisson Family of Distributions","authors":"G. Aryal, H. Yousof","doi":"10.1515/eqc-2017-0004","DOIUrl":"https://doi.org/10.1515/eqc-2017-0004","url":null,"abstract":"In this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"4 1","pages":"23 - 7"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80348004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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