Accurate higher-order likelihood inference on $$P(Y>X)$$

Giuliana Cortese () and Laura Ventura ()

Computational Statistics, 2013, vol. 28, issue 3, 1035-1059

Abstract: The stress-strength reliability $$R=P(Y>X)$$ , where $$X$$ and $$Y$$ are independent continuous random variables, has obtained wide attention in many areas of application, such as in engineering statistics and biostatistics. Classical likelihood-based inference about $$R$$ has been widely examined under various assumptions on $$X$$ and $$Y$$ . However, it is well-known that first order inference can be inaccurate, in particular when the sample size is small or in presence of unknown parameters. The aim of this paper is to illustrate higher-order likelihood-based procedures for parametric inference in small samples, which provide accurate point estimators and confidence intervals for $$R$$ . The proposed procedures are illustrated under the assumptions of Gaussian and exponential models for $$(X,Y)$$ . Moreover, simulation studies are performed in order to study the accuracy of the proposed methodology, and an application to real data is discussed. An implementation of the proposed method in the R software is provided. Copyright Springer-Verlag 2013

Keywords: Stress-strength model; Confidence interval; Modified signed log-likelihood; Higher-order likelihood inference; Small sample size; Area under the ROC curve (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00180-012-0343-z (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:compst:v:28:y:2013:i:3:p:1035-1059

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-012-0343-z

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

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