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Counting by weighing: know your numbers with confidence
Author(s) -
Liu W.,
Han Y.,
Bretz F.,
Wan F.,
Yang P.
Publication year - 2016
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/rssc.12142
Subject(s) - set (abstract data type) , confidence interval , inference , calibration , interpretation (philosophy) , confidence distribution , mathematics , statistics , data set , upper and lower bounds , confidence region , statistical inference , computer science , artificial intelligence , mathematical analysis , programming language
Summary Counting by weighing is often more efficient than counting manually, which is time consuming and prone to human errors, especially when the number of items (e.g. plant seeds, printed labels or coins) is large. Papers in the statistical literature have focused on how to count, by weighing, a random number of items that is close to a prespecified number in some sense. The paper considers the new problem, arising from a consultation with a company, of making inference about the number of 1p coins in a bag with known weight for infinitely many bags, by using the estimated distribution of coin weight from one calibration data set only. Specifically, a lower confidence bound has been constructed on the number of 1p coins for each of infinitely many future bags of 1p coins, as required by the company. As the same calibration data set is used repeatedly in the construction of all these lower confidence bounds, the interpretation of coverage frequency of the lower confidence bounds that is proposed is different from that of a usual confidence set.