Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions

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...

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Bibliographic Details
Main Authors: Eliardo Costa, Manoel Santos-Neto, Víctor Leiva
Format: Article
Language:English
Published: MDPI AG 2021-05-01
Series:Symmetry
Subjects:
Bayes risk
inverse gamma distribution
LINEX loss function
Metropolis–Hastings algorithm
R language
sampling cost
Online Access:https://www.mdpi.com/2073-8994/13/6/926
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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
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