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Thangjai W, Niwitpong SA, Niwitpong S. Estimation of the percentile of Birnbaum-Saunders distribution and its application to PM2.5 in Northern Thailand. PeerJ 2024; 12:e17019. [PMID: 38436012 PMCID: PMC10909348 DOI: 10.7717/peerj.17019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Accepted: 02/06/2024] [Indexed: 03/05/2024] Open
Abstract
The Birnbaum-Saunders distribution plays a crucial role in statistical analysis, serving as a model for failure time distribution in engineering and the distribution of particulate matter 2.5 (PM2.5) in environmental sciences. When assessing the health risks linked to PM2.5, it is crucial to give significant weight to percentile values, particularly focusing on lower percentiles, as they offer a more precise depiction of exposure levels and potential health hazards for the population. Mean and variance metrics may not fully encapsulate the comprehensive spectrum of risks connected to PM2.5 exposure. Various approaches, including the generalized confidence interval (GCI) approach, the bootstrap approach, the Bayesian approach, and the highest posterior density (HPD) approach, were employed to establish confidence intervals for the percentile of the Birnbaum-Saunders distribution. To assess the performance of these intervals, Monte Carlo simulations were conducted, evaluating them based on coverage probability and average length. The results demonstrate that the GCI approach is a favorable choice for estimating percentile confidence intervals. In conclusion, this article presents the results of the simulation study and showcases the practical application of these findings in the field of environmental sciences.
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Affiliation(s)
- Warisa Thangjai
- Department of Statistics, Ramkhamhaeng University, Bangkok, Thailand
| | - Sa-Aat Niwitpong
- Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
| | - Suparat Niwitpong
- Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
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Liu K, Balakrishnan N, He M, Xie L. Likelihood inference for Birnbaum–Saunders frailty model with an application to bone marrow transplant data. J STAT COMPUT SIM 2023. [DOI: 10.1080/00949655.2023.2174543] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Affiliation(s)
- Kai Liu
- School of Statistics and Mathematics, Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China
| | - N. Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
| | - Mu He
- Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou, People's Republic of China
| | - Lingfang Xie
- School of Finance, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China
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Puggard W, Niwitpong S, Niwitpong S. Simultaneous Confidence Intervals for All Pairwise Differences between the Coefficients of Variation of Multiple Birnbaum–Saunders Distributions. Symmetry (Basel) 2022; 14:2666. [DOI: 10.3390/sym14122666] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and has become widely employed for reliability and fatigue studies. In statistics, the coefficient of variation (CV) is employed to measure relative variation. Furthermore, comparing the CVs of several samples from BS distributions is an important approach to assess the variation among them. Herein, we propose estimation methods for the simultaneous confidence intervals (SCIs) for all pairwise differences between the CVs of multiple BS distributions based on the percentile bootstrap, the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER) based on the asymptotic confidence interval (ACI) and GCI, Bayesian credible interval, and the highest posterior density (HPD) interval. The coverage probabilities and average lengths of the proposed methods were examined via a simulation study to determine their performance. The results demonstrate that GCI and the MOVER based on the GCI method provided satisfactory performances in almost every case studied. Particulate matter ≤ 2.5 μm (PM2.5) concentration datasets from three areas in northern Thailand were used to illustrate the effectiveness of the proposed methods.
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Puggard W, Niwitpong S, Niwitpong S. Confidence Intervals for Common Coefficient of Variation of Several Birnbaum–Saunders Distributions. Symmetry (Basel) 2022; 14:2101. [DOI: 10.3390/sym14102101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
The Birnbaum–Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). Furthermore, the coefficient of variation (CV) is commonly used to analyze variation within a dataset. In some situations, the independent samples are collected from different instruments or laboratories. Consequently, it is of importance to make inference for the common CV. To this end, confidence intervals based on the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), large-sample (LS), Bayesian credible interval (BayCrI), and highest posterior density interval (HPDI) methods are proposed herein to estimate the common CV of several BS distributions. Their performances in terms of their coverage probabilities and average lengths were investigated by using Monte Carlo simulation. The simulation results indicate that the HPDI-based confidence interval outperformed the others in all of the investigated scenarios. Finally, the efficacies of the proposed confidence intervals are illustrated by applying them to real datasets of PM10 (particulate matter ≤ 10 μm) concentrations from three pollution monitoring stations in Chiang Mai, Thailand.
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Puggard W, Niwitpong S, Niwitpong S. Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions. Symmetry (Basel) 2022; 14:1492. [DOI: 10.3390/sym14071492] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) distribution. This distribution can be transform to the normal distribution, which is symmetrical. Furthermore, variance is used to examine the dispersion of the fatigue life data. However, comparing the variances of two independent samples that follow BS distributions has not previously been reported. To accomplish this, we propose methods for providing the confidence interval for the ratio of variances of two independent BS distributions based on the generalized fiducial confidence interval (GFCI), a Bayesian credible interval (BCI), and the highest posterior density (HPD) intervals based on a prior distribution with partial information (HPD-PI) and a proper prior with known hyperparameters (HPD-KH). A Monte Carlo simulation study was carried out to examine the efficacies of the methods in terms of their coverage probabilities and average lengths. The simulation results indicate that the HPD-PI performed satisfactorily for all sample sizes investigated. To illustrate the efficacies of the proposed methods with real data, they were also applied to study the confidence interval for the ratio of the variances of two 6061-T6 aluminum coupon fatigue-life datasets.
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Alam FMA, Almalki AM. On Modeling Cancer and Tuberculosis Data Using the Birnbaum–Saunders Lifetime Model Established on a Logistic Kernel. Applied Sciences 2022; 12:5000. [DOI: 10.3390/app12105000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Due to their importance in representing, explaining, and analyzing phenomena, statistical lifetime distributions are widely used in science. As a result, this paper discusses a modern lifetime model called Birnbaum–Saunders logistic distribution. This distribution extends the Birnbaum–Saunders distribution, as it has proven to be characterized by great flexibility in data modeling in practice. Different features of this distribution have been discussed. The parameters of the model are estimated using the maximum likelihood and modified moment estimation methods. To evaluate the performance of the methods, a simulation study with data contamination scenarios is presented. Finally, the new model’s flexibility is tested using real datasets.
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Martínez-Flórez G, Olmos NM, Venegas O. Unit-bimodal Birnbaum-Saunders distribution with applications. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2069260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Guillermo Martínez-Flórez
- Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Córdoba, Colombia
| | - Neveka M. Olmos
- Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile
| | - Osvaldo Venegas
- Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco, Chile
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Puggard W, Niwitpong SA, Niwitpong S. Confidence intervals for the variance and difference of variances of Birnbaum-Saunders distributions. J STAT COMPUT SIM 2022. [DOI: 10.1080/00949655.2022.2050231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Wisunee Puggard
- Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
| | - Sa-Aat Niwitpong
- Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
| | - Suparat Niwitpong
- Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
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Benites L, Maehara R, Vilca F, Marmolejo-ramos F. Finite Mixture of Birnbaum–Saunders Distributions Using the k-Bumps Algorithm. J Stat Theory Pract 2022; 16. [DOI: 10.1007/s42519-022-00245-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Balakrishnan N, Alam FMA. Maximum likelihood estimation of the parameters of student’s t Birnbaum-Saunders distribution: a comparative study. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2019.1659359] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
| | - Farouq Mohammad A. Alam
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
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Puggard W, Niwitpong S, Niwitpong S. Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions. Symmetry (Basel) 2021; 13:2130. [DOI: 10.3390/sym13112130] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The Birnbaum–Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an important descriptive statistic for explaining variation within a dataset, has not previously been used for statistical inference on a BS distribution. The aim of this study is to present four methods for constructing confidence intervals for the CV, and the difference between the CVs of BS distributions. The proposed methods are based on the generalized confidence interval (GCI), a bootstrapped confidence interval (BCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval. A Monte Carlo simulation study was conducted to evaluate their performances in terms of coverage probability and average length. The results indicate that the HPD interval was the best-performing method overall. PM 2.5 concentration data for Chiang Mai, Thailand, collected in March and April 2019, were used to illustrate the efficacies of the proposed methods, the results of which were in good agreement with the simulation study findings.
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Lu MC, Chang DS, Yang SF. Exact statistical inferences for the median of the Birnbaum–Saunders distribution. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1967352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Ming-Che Lu
- Department of Accounting, Chaoyang University of Technology, Taichung, Taiwan
| | - Dong-Shang Chang
- Department of Business Administration, National Central University, Taoyuan, Taiwan
| | - Su-Fen Yang
- Department of Statistics, National Chengchi University, Taipei, Taiwan
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Costa E, Santos-neto M, Leiva V. Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions. Symmetry (Basel) 2021; 13:926. [DOI: 10.3390/sym13060926] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
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.
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Jayalath KP. Fiducial Inference on the Right Censored Birnbaum–Saunders Data via Gibbs Sampler. Stats 2021; 4:385-99. [DOI: 10.3390/stats4020025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
In this article, we implement a flexible Gibbs sampler to make inferences for two-parameter Birnbaum–Saunders (BS) distribution in the presence of right-censored data. The Gibbs sampler is applied on the fiducial distributions of the BS parameters derived using the maximum likelihood, methods of moments, and their bias-reduced estimates. A Monte-Carlo study is conducted to make comparisons between these estimates for Type-II right censoring with various parameter settings, sample sizes, and censoring percentages. It is concluded that the bias-reduced estimates outperform the rest with increasing precision. Higher sample sizes improve the overall accuracy of all the estimates while the amount of censoring shows a negative effect. Further comparisons are made with existing methods using two real-world examples.
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Saulo H, Leão J, Leiva V, Vila R, Tomazella V. A bivariate fatigue-life regression model and its application to fracture of metallic tools. BRAZ J PROBAB STAT 2021. [DOI: 10.1214/20-bjps490] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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18
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Kim HM, Jang YH. New closed-form estimators for weighted Lindley distribution. J Korean Stat Soc 2021. [DOI: 10.1007/s42952-020-00097-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Affiliation(s)
- Renata G. Romeiro
- Departamento de Estatística, Universidade Estadual de Campinas, São Paulo, Brazil
| | - Filidor Vilca
- Departamento de Estatística, Universidade Estadual de Campinas, São Paulo, Brazil
| | - N. Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, Canada
| | - Camila Borelli Zeller
- Departamento de Estatística, Universidade Federal de Juiz de Fora, Minas Gerais, Brazil
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Affiliation(s)
| | | | - Suely Ruiz Giolo
- Department of Statistics, Federal University of Paraná, Curitiba, Paraná, Brazil
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Abstract
In this paper, we propose a bimodal extension of the Birnbaum–Saunders model by including an extra parameter. This new model is termed flexible Birnbaum–Saunders (FBS) and includes the ordinary Birnbaum–Saunders (BS) and the skew Birnbaum–Saunders (SBS) model as special cases. Its properties are studied. Parameter estimation is considered via an iterative maximum likelihood approach. Two real applications, of interest in environmental sciences, are included, which reveal that our proposal can perform better than other competing models.
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Affiliation(s)
- Helton Saulo
- Departamento de Estatística, Universidade de Brasília, DF, Brazil
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada
| | - Marcelo Bourguignon
- Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil
| | - Xiaojun Zhu
- Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, Jiangsu, P.R. China
| | - N. Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada
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Hashemi F, Naderi M, Mashinchi M. Clustering right-skewed data stream via Birnbaum–Saunders mixture models: A flexible approach based on fuzzy clustering algorithm. Appl Soft Comput 2019; 82:105539. [DOI: 10.1016/j.asoc.2019.105539] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Saulo H, Leão J, Vila R, Leiva V, Tomazella V. On mean-based bivariate Birnbaum-Saunders distributions: Properties, inference and application. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2019.1626425] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Helton Saulo
- Department of Statistics, Universidade de Brasília, Brasilia, Brazil
- Faculty of Administration, Accounting and Economics, Universidade Federal de Goias, Goiânia, Brazil
| | - Jeremias Leão
- Department of Statistics, Universidade Federal do Amazonas, Manaus, Brazil
| | - Roberto Vila
- Department of Statistics, Universidade de Brasília, Brasilia, Brazil
| | - Victor Leiva
- School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaiso, Chile
| | - Vera Tomazella
- Department of Statistics, Universidade Federal de São Carlos, São Carlos, Brazil
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Athayde E, Azevedo A, Barros M, Leiva V. Failure rate of Birnbaum–Saunders distributions: Shape, change-point, estimation and robustness. BRAZ J PROBAB STAT 2019. [DOI: 10.1214/17-bjps389] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Sha N. A New Inference Approach for Type-II Generalized Birnbaum-Saunders Distribution. Stats 2019; 2:148-63. [DOI: 10.3390/stats2010011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The Birnbaum-Saunders (BS) distribution, with its generalizations, has been successfully applied in a wide variety of fields. One generalization, type-II generalized BS (denoted as GBS-II), has been developed and attracted considerable attention in recent years. In this article, we propose a new simple and convenient procedure of inference approach for GBS-II distribution. An extensive simulation study is carried out to assess performance of the methods under various settings of parameter values with different sample sizes. Real data are analyzed for illustrative purposes to display the efficiency of the proposed method.
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Zhu X, Balakrishnan N, Saulo H. On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples. METRIKA 2019. [DOI: 10.1007/s00184-019-00707-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Abstract
As a result of the two-parameter Birnbaum–Saunders (BS) distribution being successful in modelling fatigue failure times, several extensions of this model have been explored from different aspects. In this article, we consider a progressive stress accelerated life testing for the BS model to introduce a generalized Birnbaum–Saunders (we call it Type-II GBS) distribution on the lifetime of products in the test. We outline some interesting properties of this highly flexible distribution, present the Fisher’s information in the maximum likelihood estimation method, and propose a new Bayesian approach for inference. Simulation studies are carried out to assess the performance of the methods under various settings of parameter values and sample sizes. Real data are analyzed for illustrative purposes to demonstrate the efficiency and accuracy of the proposed Bayesian method over the likelihood-based procedure.
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Abstract
In this paper, a generalization of the modified slash Birnbaum–Saunders (BS) distribution is introduced. The model is defined by using the stochastic representation of the BS distribution, where the standard normal distribution is replaced by a symmetric distribution proposed by Reyes et al. It is proved that this new distribution is able to model more kurtosis than other extensions of BS previously proposed in the literature. Closed expressions are given for the pdf (probability density functio), along with their moments, skewness and kurtosis coefficients. Inference carried out is based on modified moments method and maximum likelihood (ML). To obtain ML estimates, two approaches are considered: Newton–Raphson and EM-algorithm. Applications reveal that it has potential for doing well in real problems.
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Affiliation(s)
- Renata G. Romeiro
- Departamento de Estatística, Universidade Estadual de Campinas, São Paulo, Brazil
| | - Filidor Vilca
- Departamento de Estatística, Universidade Estadual de Campinas, São Paulo, Brazil
| | - N. Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada
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Affiliation(s)
- M. E. Ghitany
- Department of Statistics and Operations Research, Faculty of Science, Kuwait University, Safat, Kuwait
| | - Pingfan Song
- School of Economics, Hefei University of Technology, Hefei, People's Republic of China
| | - Shaochen Wang
- School of Mathematics, South China University of Technology, Guangzhou, People's Republic of China
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Fang L, Balakrishnan N. Ordering properties of the smallest order statistics from generalized Birnbaum–Saunders models with associated random shocks. METRIKA 2018; 81:19-35. [DOI: 10.1007/s00184-017-0632-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Affiliation(s)
- Naijun Sha
- Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, USA
| | - Tun Lee Ng
- Department of Statistics, University of Wisconsin, Madison, WI, USA
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Affiliation(s)
- Longxiang Fang
- Department of Mathematics and Computer Science, Anhui Normal University, Wuhu People's Republic of China
| | - Xiaojun Zhu
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
| | - N. Balakrishnan
- Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou People's Republic of China
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Zhang Y, Lu X, Desmond AF. Variable Selection in a Log–Linear Birnbaum–Saunders Regression Model for High-Dimensional Survival Data via the Elastic-Net and Stochastic EM. Technometrics 2016. [DOI: 10.1080/00401706.2015.1133457] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Yukun Zhang
- Department of Mathematics and Statistics, University of Calgary 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Xuewen Lu
- Department of Mathematics and Statistics, University of Calgary 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Anthony F. Desmond
- Department of Mathematics and Statistics, University of Guelph 50 Stone Road East, Guelph, Ontario N1G 2W1, Canada
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Affiliation(s)
- Neveka M. Olmos
- Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile
| | - Guillermo Martínez-Flórez
- Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Córdoba, Colombia
| | - Heleno Bolfarine
- Departamento de Estatítica, IME, Universidade de São Paulo, São Paulo, Brazil
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Affiliation(s)
- Xu Guo
- College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China
| | - Hecheng Wu
- College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China
| | - Gaorong Li
- Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing, People's Republic of China
| | - Qiuyue Li
- College of Science, China Agricultural University, Beijing, People's Republic of China
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Fang L, Zhu X, Balakrishnan N. Stochastic comparisons of parallel and series systems with heterogeneous Birnbaum–Saunders components. Stat Probab Lett 2016. [DOI: 10.1016/j.spl.2016.01.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Moreno Arenas G, Martínez Flórez G, Barrera Causil C. Proportional Hazard Birnbaum-Saunders Distribution With Application to the Survival Data Analysis. Rev colomb estad 2016. [DOI: 10.15446/rce.v39n1.55145] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Abstract
<p>Birnbaum Saunders (1969b) used a probability distribution to explain the lifetime data and stress produced in materials. Based on this distribution, we propose a generalization of the Birnbaum-Saunders distribution, referred to as the proportional hazard Birnbaum-Saunders distribution, which includes a new parameter that provides more flexibility in terms of skewness and kurtosis than existing models. We derive the main properties of the model. We discuss maximum likelihood estimation of the model parameters. As a natural step, we define the log-linear proportional hazard Birnbaum-Saunders regression model. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model. The results showed that the proportional hazard Birnbaum-Saunders model can be used quite effectively in analyzing survival data, reliability problems and fatigue life studies.</p>
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Yang Y, Ng HKT, Balakrishnan N. A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature. Comput Stat 2016; 31:609-41. [DOI: 10.1007/s00180-015-0586-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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