A unified method for constructing expectation tolerance intervals

Christopher Withers and Saralees Nadarajah ()

Statistical Papers, 2014, vol. 55, issue 4, 965 pages

Abstract: Given a random sample of size $$n$$ n with mean $$\overline{X} $$ X ¯ and standard deviation $$s$$ s from a symmetric distribution $$F(x; \mu , \sigma )=F_{0} (( x- \mu ) / \sigma ) $$ F ( x ; μ , σ ) = F 0 ( ( x - μ ) / σ ) with $$F_0$$ F 0 known, and $$X \sim F(x;\; \mu , \sigma )$$ X ∼ F ( x ; μ , σ ) independent of the sample, we show how to construct an expansion $$ a_n^{\prime }=\sum _{i=0}^\infty \ c_i \ n^{-i} $$ a n ′ = ∑ i = 0 ∞ c i n - i such that $$\overline{X} - s a_n^{\prime } > X > \overline{X} + s a_n^{\prime } $$ X ¯ - s a n ′ > X > X ¯ + s a n ′ with a given probability $$\beta $$ β . The practical value of this result is illustrated by simulation and using a real data set. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Expectation tolerance intervals; Location-scale families; Simulation (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s00362-013-0543-9 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:55:y:2014:i:4:p:951-965

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-013-0543-9

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().