{"title":"Fisher information for generalized Rayleigh distribution in ranked set sampling design with application to parameter estimation","authors":"Bing-liang Shen, Shuo Wang, Wang-xue Chen, Meng Chen","doi":"10.1007/s11766-022-4450-5","DOIUrl":null,"url":null,"abstract":"<div><p>In the current paper, we considered the Fisher information matrix from the generalized Rayleigh distribution (GR) distribution in ranked set sampling (RSS). The numerical results show that the ranked set sample carries more information about <i>λ</i> and <i>α</i> than a simple random sample of equivalent size. In order to give more insight into the performance of RSS with respect to (w.r.t.) simple random sampling (SRS), a modified unbiased estimator and a modified best linear unbiased estimator (BLUE) of scale and shape <i>λ</i> and <i>α</i> from GR distribution in SRS and RSS are studied. The numerical results show that the modified unbiased estimator and the modified BLUE of <i>λ</i> and <i>α</i> in RSS are significantly more efficient than the ones in SRS.</p></div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"37 4","pages":"615 - 630"},"PeriodicalIF":1.0000,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11766-022-4450-5.pdf","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-022-4450-5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
In the current paper, we considered the Fisher information matrix from the generalized Rayleigh distribution (GR) distribution in ranked set sampling (RSS). The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size. In order to give more insight into the performance of RSS with respect to (w.r.t.) simple random sampling (SRS), a modified unbiased estimator and a modified best linear unbiased estimator (BLUE) of scale and shape λ and α from GR distribution in SRS and RSS are studied. The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.
期刊介绍：
Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects.
The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry.
Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.
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