Aykroyd, RG orcid.org/0000-0003-3700-0816, Leiva, V and Marchant, C (2018) Multivariate Birnbaum-Saunders Distributions: Modelling and Applications. Risks, 6 (1). 21. ISSN 2227-9091
Abstract
Since its origins and numerous applications in material science, the Birnbaum–Saunders family of distributions has now found widespread uses in some areas of the applied sciences such as agriculture, environment and medicine, as well as in quality control, among others. It is able to model varied data behaviour and hence provides a flexible alternative to the most usual distributions. The family includes Birnbaum–Saunders and log-Birnbaum–Saunders distributions in univariate and multivariate versions. There are now well-developed methods for estimation and diagnostics that allow in-depth analyses. This paper gives a detailed review of existing methods and of relevant literature, introducing properties and theoretical results in a systematic way. To emphasise the range of suitable applications, full analyses are included of examples based on regression and diagnostics in material science, spatial data modelling in agricultural engineering and control charts for environmental monitoring. However, potential future uses in new areas such as business, economics, finance and insurance are also discussed. This work is presented to provide a full tool-kit of novel statistical models and methods to encourage other researchers to implement them in these new areas. It is expected that the methods will have the same positive impact in the new areas as they have had elsewhere.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0). |
Keywords: | asymmetric distributions; control charts; diagnostics; multivariate methods; non-normality; regression; R software; spatial models |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Mar 2018 12:44 |
Last Modified: | 19 Mar 2018 09:36 |
Status: | Published |
Publisher: | MDPI |
Identification Number: | 10.3390/risks6010021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:128114 |