{"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}
{"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}