Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions
The fatigue-life or Birnbaum–Saunders distribution is an asymmetrical model that has been widely applied in several areas of science and mainly in reliability. Although diverse methodologies related to this distribution have been proposed, the problem of determining the optimal sample size when esti...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2021-05-01
|
Series: | Symmetry |
Subjects: | |
Online Access: | https://www.mdpi.com/2073-8994/13/6/926 |
id |
doaj-7a4bcb2f23a24a8ca609017f9d8f8ca3 |
---|---|
record_format |
Article |
spelling |
doaj-7a4bcb2f23a24a8ca609017f9d8f8ca32021-06-01T00:51:13ZengMDPI AGSymmetry2073-89942021-05-011392692610.3390/sym13060926Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss FunctionsEliardo Costa0Manoel Santos-Neto1Víctor Leiva2Department of Statistics, Universidade Federal do Rio Grande do Norte, Natal 59078-970, BrazilDepartment of Statistics, Universidade Federal de Campina Grande, Campina Grande 58429-900, BrazilSchool of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, ChileThe fatigue-life or Birnbaum–Saunders distribution is an asymmetrical model that has been widely applied in several areas of science and mainly in reliability. Although diverse methodologies related to this distribution have been proposed, the problem of determining the optimal sample size when estimating its mean has not yet been studied. In this paper, we derive a methodology to determine the optimal sample size under a decision-theoretic approach. In this approach, we consider symmetric and asymmetric loss functions for point and interval inference. Computational tools in the R language were implemented to use this methodology in practice. An illustrative example with real data is also provided to show potential applications.https://www.mdpi.com/2073-8994/13/6/926Bayes riskinverse gamma distributionLINEX loss functionMetropolis–Hastings algorithmR languagesampling cost |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Eliardo Costa Manoel Santos-Neto Víctor Leiva |
spellingShingle |
Eliardo Costa Manoel Santos-Neto Víctor Leiva Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions Symmetry Bayes risk inverse gamma distribution LINEX loss function Metropolis–Hastings algorithm R language sampling cost |
author_facet |
Eliardo Costa Manoel Santos-Neto Víctor Leiva |
author_sort |
Eliardo Costa |
title |
Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions |
title_short |
Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions |
title_full |
Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions |
title_fullStr |
Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions |
title_full_unstemmed |
Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions |
title_sort |
optimal sample size for the birnbaum–saunders distribution under decision theory with symmetric and asymmetric loss functions |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2021-05-01 |
description |
The fatigue-life or Birnbaum–Saunders distribution is an asymmetrical model that has been widely applied in several areas of science and mainly in reliability. Although diverse methodologies related to this distribution have been proposed, the problem of determining the optimal sample size when estimating its mean has not yet been studied. In this paper, we derive a methodology to determine the optimal sample size under a decision-theoretic approach. In this approach, we consider symmetric and asymmetric loss functions for point and interval inference. Computational tools in the R language were implemented to use this methodology in practice. An illustrative example with real data is also provided to show potential applications. |
topic |
Bayes risk inverse gamma distribution LINEX loss function Metropolis–Hastings algorithm R language sampling cost |
url |
https://www.mdpi.com/2073-8994/13/6/926 |
work_keys_str_mv |
AT eliardocosta optimalsamplesizeforthebirnbaumsaundersdistributionunderdecisiontheorywithsymmetricandasymmetriclossfunctions AT manoelsantosneto optimalsamplesizeforthebirnbaumsaundersdistributionunderdecisiontheorywithsymmetricandasymmetriclossfunctions AT victorleiva optimalsamplesizeforthebirnbaumsaundersdistributionunderdecisiontheorywithsymmetricandasymmetriclossfunctions |
_version_ |
1721413757940269056 |