Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Birnbaum and Saunders introduced a two-parameter lifetime distribution to model fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate and matrix-variate cases. More than two hundred papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and at the same time indicate several open problems that could be considered for further research.

[1]  V. Leiva,et al.  Failure rate of Birnbaum–Saunders distributions: Shape, change-point, estimation and robustness , 2019, Brazilian Journal of Probability and Statistics.

[2]  Helton Saulo,et al.  Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data , 2018, Statistics in medicine.

[3]  Miguel Angel Uribe-Opazo,et al.  Birnbaum-Saunders spatial regression models: Diagnostics and application to chemical data , 2018, Chemometrics and Intelligent Laboratory Systems.

[4]  Miguel A. Uribe-Opazo,et al.  Kriging with external drift in a Birnbaum–Saunders geostatistical model , 2018, Stochastic Environmental Research and Risk Assessment.

[5]  Helton Saulo,et al.  On a tobit–Birnbaum–Saunders model with an application to medical data , 2018 .

[6]  Renata G. Romeiro,et al.  A robust multivariate Birnbaum–Saunders distribution: EM estimation , 2018 .

[7]  Smail Adjabi,et al.  Birnbaum–Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy tailed data , 2017, Computational Statistics.

[8]  J. Ramalho‐Santos.  Data , 2018, Nature.

[9]  Francisco Cribari‐Neto,et al.  Bimodal Birnbaum–Saunders generalized autoregressive score model , 2018 .

[10]  R. Aykroyd,et al.  L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data , 2018 .

[11]  S. Balamurali,et al.  Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution , 2018 .

[12]  Víctor Leiva,et al.  Robust multivariate control charts based on Birnbaum–Saunders distributions , 2018 .

[13]  N. Balakrishnan,et al.  Stochastic ordering of minima and maxima from heterogeneous bivariate Birnbaum–Saunders random vectors , 2018 .

[14]  Víctor Leiva,et al.  Multivariate Generalized Birnbaum-Saunders Models Applied to Case Studies in Bio-Engineering and Industry , 2018 .

[15]  N. Balakrishnan.  SEMI-PARAMETRIC LIKELIHOOD INFERENCE FOR BIRNBAUM – SAUNDERS FRAILTY MODEL , 2018 .

[16]  N. Balakrishnan,et al.  Ordering properties of the smallest order statistics from generalized Birnbaum–Saunders models with associated random shocks , 2018 .

[17]  Robert G. Aykroyd,et al.  Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data , 2019 .

[18]  D. Kundu.  On Multivariate Log Birnbaum-Saunders Distribution , 2017 .

[19]  Filidor V. Vilca,et al.  Modified slash Birnbaum-Saunders distribution , 2017 .

[20]  H. Bolfarine,et al.  The Log-Linear Birnbaum-Saunders Power Model , 2017 .

[21]  Filidor V. Vilca,et al.  Bayesian inference for sinh-normal/independent nonlinear regression models , 2017 .

[22]  Jon G. McGowan,et al.  Use of Birnbaum-Saunders distribution for estimating wind speed and wind power probability distributions: A review , 2017 .

[23]  Luis Hernando Vanegas,et al.  Log-symmetric regression models under the presence of non-informative left- or right-censored observations , 2017 .

[24]  N. Sha,et al.  Bayesian inference for Birnbaum–Saunders distribution and its generalization , 2017 .

[25]  D. Dey,et al.  Scale mixtures log-Birnbaum–Saunders regression models with censored data: a Bayesian approach , 2017 .

[26]  Gaorong Li,et al.  Inference for the common mean of several Birnbaum–Saunders populations , 2017 .

[27]  Xiaojun Zhu,et al.  On moment-type estimators for a class of log-symmetric distributions , 2017, Comput. Stat..

[28]  Heleno Bolfarine,et al.  Bimodal Birnbaum–Saunders distribution with applications to non negative measurements , 2017 .

[29]  N. Balakrishnan,et al.  Estimation in generalized bivariate Birnbaum–Saunders models , 2017 .

[30]  Yimin Shi,et al.  Inference for Constant-Stress Accelerated Life Tests With Dependent Competing Risks From Bivariate Birnbaum–Saunders Distribution Based on Adaptive Progressively Hybrid Censoring , 2017, IEEE Transactions on Reliability.

[31]  N. Balakrishnan,et al.  On a new class of skewed Birnbaum-Saunders models , 2017 .

[32]  Helton Saulo,et al.  Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data , 2017, Biometrical journal. Biometrische Zeitschrift.

[33]  D. Kundu,et al.  On Bivariate Birnbaum–Saunders Distribution , 2017 .

[34]  Helton Saulo,et al.  Environmental Applications Based on Birnbaum–Saunders Models , 2017 .

[35]  M. Bourguignon,et al.  THE TRANSMUTED BIRNBAUM-SAUNDERS DISTRIBUTION , 2017 .

[36]  Helton Saulo,et al.  A methodology based on the Birnbaum-Saunders distribution for reliability analysis applied to nano-materials , 2017, Reliab. Eng. Syst. Saf..

[37]  Xuewen Lu,et al.  Variable Selection in a Log–Linear Birnbaum–Saunders Regression Model for High-Dimensional Survival Data via the Elastic-Net and Stochastic EM , 2016, Technometrics.

[38]  Ancha Xu,et al.  Fiducial inference for Birnbaum-Saunders distribution , 2016 .

[39]  Wei Yu,et al.  Confidence interval estimation by a joint pivot method , 2016, Comput. Stat..

[40]  Francisco José de A. Cysneiros,et al.  A Multivariate Log-Linear Model for Birnbaum-Saunders Distributions , 2016, IEEE Transactions on Reliability.

[41]  N. Balakrishnan,et al.  Stochastic comparisons of parallel and series systems with heterogeneous Birnbaum–Saunders components , 2016 .

[42]  Narayanaswamy Balakrishnan,et al.  A bivariate Birnbaum-Saunders regression model , 2016, Comput. Stat. Data Anal..

[43]  Fernando Rojas Ruiz,et al.  Inventory management for new products with triangularly distributed demand and lead-time , 2016, Comput. Oper. Res..

[44]  Marcelino A. R. Pascoa,et al.  An extended Birnbaum–Saunders distribution: Theory, estimation, and applications , 2016 .

[45]  Juan F. Vivanco,et al.  Diagnostics in multivariate generalized Birnbaum-Saunders regression models , 2016 .

[46]  Min Wang,et al.  Bayesian analysis of Birnbaum–Saunders distribution via the generalized ratio-of-uniforms method , 2016, Comput. Stat..

[47]  Gauss M. Cordeiro,et al.  A model with long-term survivors: negative binomial Birnbaum-Saunders , 2016 .

[48]  Artur J. Lemonte.  Robust inference for Birnbaum–Saunders regressions , 2016 .

[49]  Emilio Porcu,et al.  On a nonlinear Birnbaum–Saunders model based on a bivariate construction and its characteristics , 2016 .

[50]  Víctor Leiva,et al.  A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution , 2016 .

[51]  Víctor Leiva,et al.  Reparameterized Birnbaum-Saunders regression models with varying precision , 2016 .

[52]  Víctor Leiva,et al.  Genesis of the Birnbaum–Saunders Distribution , 2016 .

[53]  Miguel Angel Uribe-Opazo,et al.  Birnbaum–Saunders spatial modelling and diagnostics applied to agricultural engineering data , 2016, Stochastic Environmental Research and Risk Assessment.

[54]  M. Ivette Gomes,et al.  Extreme value Birnbaum–Saunders regression models applied to environmental data , 2016, Stochastic Environmental Research and Risk Assessment.

[55]  Víctor Leiva,et al.  On matrix-variate Birnbaum–Saunders distributions and their estimation and application , 2015 .

[56]  Chanseok Park,et al.  Simple robust parameter estimation for the Birnbaum-Saunders distribution , 2015 .

[57]  Víctor Leiva,et al.  The Birnbaum-Saunders Distribution , 2015 .

[58]  Fabrizio Ruggeri,et al.  A criterion for environmental assessment using Birnbaum–Saunders attribute control charts , 2015 .

[59]  Peter Wanke,et al.  Exploring the Potential Use of the Birnbaum-Saunders Distribution in Inventory Management , 2015 .

[60]  Fernando Marmolejo-Ramos,et al.  Modeling neural activity with cumulative damage distributions , 2015, Biological Cybernetics.

[61]  Jorge Alberto Achcar,et al.  Bayesian Estimation for the Birnbaum-Saunders distribution in the presence of censored data , 2015, IEEE Latin America Transactions.

[62]  D. Kundu,et al.  A Multivariate Birnbaum-Saunders Distribution Based on the Multivariate Skew Normal Distribution , 2015 .

[63]  Ahad Jamalizadeh,et al.  Multivariate normal mean–variance mixture distribution based on Birnbaum–Saunders distribution , 2015 .

[64]  Debasis Kundu.  Bivariate sinh-normal distribution and a related model , 2015 .

[65]  Debasis Kundu,et al.  Bivariate log Birnbaum–Saunders distribution , 2015 .

[66]  Xiaojun Zhu,et al.  Birnbaum–Saunders distribution based on Laplace kernel and some properties and inferential issues , 2015 .

[67]  N. Balakrishnan,et al.  Inference for the Birnbaum–Saunders Lifetime Regression Model with Applications , 2015, Commun. Stat. Simul. Comput..

[68]  D. Kundu,et al.  On bivariate and a mixture of bivariate Birnbaum–Saunders distributions , 2015 .

[69]  N. Balakrishnan,et al.  Inference for the bivariate Birnbaum–Saunders lifetime regression model and associated inference , 2015 .

[70]  Artur J. Lemonte,et al.  Multivariate Birnbaum–Saunders distribution: properties and associated inference , 2015 .

[71]  Ramesh C. Gupta.  RELIABILITY STUDIES OF BIVARIATE BIRNBAUM–SAUNDERS DISTRIBUTION , 2015, Probability in the Engineering and Informational Sciences.

[72]  Helton Saulo,et al.  Monitoring Environmental Risk by a Methodology Based on Control Charts , 2015 .

[73]  Víctor Leiva,et al.  Optimization of Contribution Margins in Food Services by Modeling Independent Component Demand , 2015 .

[74]  Alessia Dorigoni,et al.  Inverse Gaussian Distribution , 2015 .

[75]  Narayanaswamy Balakrishnan,et al.  The bivariate Sinh-Elliptical distribution with applications to Birnbaum-Saunders distribution and associated regression and measurement error models , 2014, Comput. Stat. Data Anal..

[76]  Gauss M. Cordeiro,et al.  The exponentiated generalized Birnbaum-Saunders distribution , 2014, Appl. Math. Comput..

[77]  Helton Saulo,et al.  A family of autoregressive conditional duration models applied to financial data , 2014, Comput. Stat. Data Anal..

[78]  Gauss M. Cordeiro,et al.  The Poisson Birnbaum–Saunders model with long-term survivors , 2014 .

[79]  Xiaojun Zhu,et al.  On the existence and uniqueness of the maximum likelihood estimates of the parameters of Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples , 2014 .

[80]  Lixing Zhu,et al.  Comparison of several Birnbaum–Saunders distributions , 2014 .

[81]  H. Bolfarine,et al.  An alpha-power extension for the Birnbaum–Saunders distribution , 2014 .

[82]  N. Balakrishnan,et al.  Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties , 2014, J. Multivar. Anal..

[83]  N. Balakrishnan,et al.  An improved method of estimation for the parameters of the Birnbaum–Saunders distribution , 2014 .

[84]  G. Cordeiro,et al.  The Kummer beta Birnbaum-Saunders: An alternative fatigue life distribution , 2014 .

[85]  Muhammad Aslam,et al.  Capability indices for Birnbaum–Saunders processes applied to electronic and food industries , 2014 .

[86]  Víctor Leiva,et al.  Goodness-of-Fit Tests for the Birnbaum-Saunders Distribution With Censored Reliability Data , 2014, IEEE Transactions on Reliability.

[87]  Manuel Galea,et al.  Diagnostics in Birnbaum-Saunders accelerated life models with an application to fatigue data , 2014 .

[88]  Víctor Leiva,et al.  Birnbaum–Saunders statistical modelling: a new approach , 2014 .

[89]  Narayanaswamy Balakrishnan,et al.  A robust extension of the bivariate Birnbaum-Saunders distribution and associated inference , 2014, J. Multivar. Anal..

[90]  Narayanaswamy Balakrishnan,et al.  The Art of Progressive Censoring , 2014 .

[91]  V. Leiva,et al.  A REPARAMETERIZED BIRNBAUM – SAUNDERS DISTRIBUTION AND ITS MOMENTS , ESTIMATION AND APPLICATIONS , 2014 .

[92]  Artur J. Lemonte.  Multivariate Birnbaum–Saunders regression model , 2013 .

[93]  J. Zhao,et al.  Robust explicit estimation of the two-parameter Birnbaum–Saunders distribution , 2013 .

[94]  Artur J. Lemonte.  A new extended Birnbaum-Saunders regression model for lifetime modeling , 2013, Comput. Stat. Data Anal..

[95]  Helton Saulo,et al.  Generalized Birnbaum-Saunders kernel density estimators and an analysis of financial data , 2013, Comput. Stat. Data Anal..

[96]  Debasis Kundu,et al.  Inference and optimal censoring schemes for progressively censored Birnbaum–Saunders distribution , 2013 .

[97]  Ali I. Genç.  The generalized T Birnbaum–Saunders family , 2013 .

[98]  N. Balakrishnan,et al.  A SIMPLE AND EFFICIENT METHOD OF ESTIMATION OF THE PARAMETERS OF A BIVARIATE BIRNBAUM-SAUNDERS DISTRIBUTION BASED ON TYPE-II CENSORED SAMPLES , 2013 .

[99]  Artur J. Lemonte.  A new extension of the Birnbaum–Saunders distribution , 2013 .

[100]  Debasis Kundu,et al.  Generalized multivariate Birnbaum-Saunders distributions and related inferential issues , 2013, J. Multivar. Anal..

[101]  Víctor Leiva,et al.  On a Birnbaum–Saunders distribution arising from a non-homogeneous Poisson process , 2013 .

[102]  Flávio Augusto Ziegelmann,et al.  A nonparametric method for estimating asymmetric densities based on skewed Birnbaum–Saunders distributions applied to environmental data , 2013, Stochastic Environmental Research and Risk Assessment.

[103]  S. Nadarajah,et al.  Ratios of Birnbaum-Saunders Random Variables , 2013 .

[104]  Víctor Leiva,et al.  Air contaminant statistical distributions with application to PM10 in Santiago, Chile. , 2013, Reviews of environmental contamination and toxicology.

[105]  Francisco Cribari-Neto,et al.  Computational Statistics and Data Analysis Improved Birnbaum–saunders Inference under Type Ii Censoring , 2022 .

[106]  Bing Xing Wang,et al.  Generalized interval estimation for the Birnbaum-Saunders distribution , 2012, Comput. Stat. Data Anal..

[107]  M. Ivette Gomes,et al.  The extreme value Birnbaum-Saunders model, its moments and an application in biometry , 2012 .

[108]  Narayanaswamy Balakrishnan,et al.  Shape and change point analyses of the Birnbaum-Saunders-t hazard rate and associated estimation , 2012, Comput. Stat. Data Anal..

[109]  Feng-Chang Xie,et al.  Diagnostic analysis for heterogeneous log-Birnbaum–Saunders regression models , 2012 .

[110]  Víctor Leiva,et al.  Fatigue Statistical Distributions Useful for Modeling Diameter and Mortality of Trees , 2012 .

[111]  Alexandre G. Patriota,et al.  On scale-mixture Birnbaum–Saunders distributions , 2012 .

[112]  Francisco José de A. Cysneiros,et al.  Diagnostic procedures in Birnbaum-Saunders nonlinear regression models , 2012, Comput. Stat. Data Anal..

[113]  Víctor Leiva,et al.  On an extreme value version of the Birnbaum-Saunders distribution , 2012 .

[114]  Gauss M. Cordeiro,et al.  Bartlett corrections in Birnbaum–Saunders nonlinear regression models , 2012 .

[115]  Víctor Leiva,et al.  About Birnbaum–Saunders Distributions Based on the Johnson System , 2012 .

[116]  Francisco Louzada,et al.  The Geometric Birnbaum–Saunders regression model with cure rate , 2012 .

[117]  Gauss M. Cordeiro,et al.  A log-linear regression model for the β-Birnbaum-Saunders distribution with censored data , 2012, Comput. Stat. Data Anal..

[118]  Narayanaswamy Balakrishnan,et al.  Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions , 2012, J. Multivar. Anal..

[119]  Xuewen Lu,et al.  A mixed effects log-linear model based on the Birnbaum-Saunders distribution , 2012, Comput. Stat. Data Anal..

[120]  Artur J. Lemonte.  A log-Birnbaum–Saunders regression model with asymmetric errors , 2010, 1009.0888.

[121]  Gilberto A. Paula,et al.  Robust statistical modeling using the Birnbaum-Saunders- t distribution applied to insurance , 2012 .

[122]  Heleno Bolfarine,et al.  Epsilon Birnbaum–Saunders distribution family: properties and inference , 2011 .

[123]  Cristian Villegas,et al.  Birnbaum-Saunders Mixed Models for Censored Reliability Data Analysis , 2011, IEEE Transactions on Reliability.

[124]  Filidor V. Vilca,et al.  Influence analysis in skew-Birnbaum–Saunders regression models and applications , 2011 .

[125]  Artur J. Lemonte.  Covariance matrix formula for Birnbaum–Saunders regression models , 2011 .

[126]  Yincai Tang,et al.  Bayesian analysis of Birnbaum-Saunders distribution with partial information , 2011, Comput. Stat. Data Anal..

[127]  Narayanaswamy Balakrishnan,et al.  On some mixture models based on the BirnbaumSaunders distribution and associated inference , 2011 .

[128]  Rafael B. A. Farias,et al.  Bayesian inference for the Birnbaum–Saunders nonlinear regression model , 2011, Stat. Methods Appl..

[129]  Víctor Leiva,et al.  Modeling wind energy flux by a Birnbaum–Saunders distribution with an unknown shift parameter , 2011 .

[130]  Chi-Hyuck Jun,et al.  New acceptance sampling plans based on life tests for Birnbaum–Saunders distributions , 2011 .

[131]  Narayanaswamy Balakrishnan,et al.  Estimation of extreme percentiles in Birnbaum-Saunders distributions , 2011, Comput. Stat. Data Anal..

[132]  Manuel Galea,et al.  Influence diagnostics on the coefficient of variation of elliptically contoured distributions , 2011 .

[133]  Gauss M. Cordeiro,et al.  The beta-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling , 2011, Comput. Stat. Data Anal..

[134]  Feng-Chang Xie,et al.  Diagnostics analysis for log‐Birnbaum–Saunders regression models with censored data , 2011 .

[135]  Artur J. Lemonte,et al.  Signed likelihood ratio tests in the BirnbaumSaunders regression model , 2011 .

[136]  Artur J. Lemonte,et al.  Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples , 2010, Comput. Stat. Data Anal..

[137]  Artur J. Lemonte,et al.  Size and power properties of some tests in the Birnbaum-Saunders regression model , 2011, Comput. Stat. Data Anal..

[138]  Alexandre G. Patriota,et al.  Influence diagnostics in Birnbaum–Saunders nonlinear regression models , 2009, 0904.4139.

[139]  Gilberto A. Paula,et al.  On estimation and influence diagnostics for log-Birnbaum–Saunders Student-t regression models: Full Bayesian analysis , 2010 .

[140]  Chad R. Bhatti,et al.  The Birnbaum-Saunders autoregressive conditional duration model , 2010, Math. Comput. Simul..

[141]  Gauss M. Cordeiro,et al.  Asymptotic skewness in Birnbaum–Saunders nonlinear regression models , 2010 .

[142]  Samuel Kotz,et al.  Two New Mixture Models Related to the Inverse Gaussian Distribution , 2010 .

[143]  Xuewen Lu,et al.  Estimation of the Birnbaum-Saunders regression model with current status data , 2010, Comput. Stat. Data Anal..

[144]  Simos G. Meintanis.  Inference procedures for the Birnbaum-Saunders distribution and its generalizations , 2010, Comput. Stat. Data Anal..

[145]  George Christakos,et al.  An extended Birnbaum–Saunders model and its application in the study of environmental quality in Santiago, Chile , 2010 .

[146]  Narayanaswamy Balakrishnan,et al.  A Skewed Sinh-Normal Distribution and Its Properties and Application to Air Pollution , 2010 .

[147]  Tzong-Ru Tsai,et al.  Acceptance Sampling Plans from Truncated Life Tests Based on the Birnbaum–Saunders Distribution for Percentiles , 2009, Commun. Stat. Simul. Comput..

[148]  Silvia L.P. Ferrari,et al.  Small-Sample Corrections for Score Tests in Birnbaum–Saunders Regressions , 2009, 0905.0668.

[149]  Francisco Cribari-Neto,et al.  Improved likelihood inference in Birnbaum-Saunders regressions , 2008, Comput. Stat. Data Anal..

[150]  Yincai Tang,et al.  Computational Statistics and Data Analysis Reference Analysis for Birnbaum–saunders Distribution , 2022 .

[151]  Debasis Kundu,et al.  Bivariate Birnbaum-Saunders distribution and associated inference , 2010, J. Multivar. Anal..

[152]  S. Ejaz Ahmed,et al.  A TRUNCATED VERSION OF THE BIRNBAUM-SAUNDERS DISTRIBUTION WITH AN APPLICATION IN FINANCIAL RISK , 2010 .

[153]  Samuel Kotz,et al.  A UNIFIED MIXTURE MODEL BASED ON THE INVERSE GAUSSIAN DISTRIBUTION , 2010 .

[154]  Bhaswati Mukherjee,et al.  Bayes Analysis and Comparison of Accelerated Weibull and Accelerated Birnbaum–Saunders Models , 2009 .

[155]  V. Leiva,et al.  On a length-biased life distribution based on the sinh-normal model , 2009 .

[156]  Harvey Fletcher.  A Verification Of The Theory Of Brownian Movements And A Direct Determination Of The Value Of NE For Gaseous Ionization , 2009 .

[157]  S. Upadhyay,et al.  Accelerated test system strength models based on Birnbaum–Saunders distribution: a complete Bayesian analysis and comparison , 2009, Lifetime data analysis.

[158]  José M. Angulo,et al.  A length-biased version of the Birnbaum-Saunders distribution with application in water quality , 2009 .

[159]  Víctor Leiva,et al.  A Non-Central Version of the Birnbaum-Saunders Distribution for Reliability Analysis , 2009, IEEE Transactions on Reliability.

[160]  Heleno Bolfarine,et al.  An extension of the generalized Birnbaum-Saunders distribution , 2009 .

[161]  Gilberto A. Paula,et al.  An R implementation for generalized Birnbaum-Saunders distributions , 2009, Comput. Stat. Data Anal..

[162]  Gauss M. Cordeiro,et al.  Birnbaum-Saunders nonlinear regression models , 2009, Comput. Stat. Data Anal..

[163]  Narayanaswamy Balakrishnan,et al.  Mixture inverse Gaussian distributions and its transformations, moments and applications , 2009 .

[164]  Narayanaswamy Balakrishnan,et al.  Estimation in the Birnbaum-Saunders distribution based on scale-mixture of normals and the EM-algorithm , 2009 .

[165]  G. Rodríguez-Yam,et al.  Estimation of parameters for a Birnbaum–Saunders regression model with censored data , 2008 .

[166]  Pranab Kumar Sen,et al.  Random number generators for the generalized Birnbaum–Saunders distribution , 2008 .

[167]  V. Leiva,et al.  A new three-parameter extension of the inverse Gaussian distribution , 2008 .

[168]  Chanseok Park,et al.  A bootstrap control chart for Birnbaum–Saunders percentiles , 2008, Qual. Reliab. Eng. Int..

[169]  Stochastic Orders , 2008 .

[170]  Gilberto A. Paula,et al.  Generalized Birnbaum‐Saunders distributions applied to air pollutant concentration , 2008 .

[171]  Víctor Leiva,et al.  A new class of survival regression models with heavy-tailed errors: robustness and diagnostics , 2008, Lifetime data analysis.

[172]  Rafał Podlaski,et al.  Characterization of diameter distribution data in near-natural forests using the Birnbaum–Saunders distribution , 2008 .

[173]  Narayanaswamy Balakrishnan,et al.  The Generalized Birnbaum–Saunders Distribution and Its Theory, Methodology, and Application , 2008 .

[174]  Francisco Cribari-Neto,et al.  Bootstrap-based improved estimators for the two-parameter Birnbaum–Saunders distribution , 2008 .

[175]  Francisco Cribari-Neto,et al.  On Birnbaum-Saunders inference , 2007, Comput. Stat. Data Anal..

[176]  Debasis Kundu,et al.  On the hazard function of Birnbaum-Saunders distribution and associated inference , 2008, Comput. Stat. Data Anal..

[177]  Intervalos de confianza vía verosimilitud relativa de los parámetros de la distribución Birnbaum-Saunders Confidence Intervals for the Parameters of the Birnbaum-Saunders Distribution via Relative likelihood , 2008 .

[178]  S. E. Ahmed,et al.  Parametric estimation for the Birnbaum-saunders Lifetime Distribution based on a new parametrization , 2008 .

[179]  Narayanaswamy Balakrishnan,et al.  Lifetime analysis based on the generalized Birnbaum-Saunders distribution , 2008, Comput. Stat. Data Anal..

[180]  José A. Díaz-García,et al.  A new family of life distributions for dependent data: Estimation , 2007, Comput. Stat. Data Anal..

[181]  Gilberto A. Paula,et al.  Influence diagnostics in log-Birnbaum-Saunders regression models with censored data , 2007, Comput. Stat. Data Anal..

[182]  Narayanaswamy Balakrishnan,et al.  Progressive censoring methodology: an appraisal , 2007 .

[183]  Narayanaswamy Balakrishnan,et al.  Acceptance Sampling Plans from Truncated Life Tests Based on the Generalized Birnbaum–Saunders Distribution , 2007, Commun. Stat. Simul. Comput..

[184]  Feng-Chang Xie,et al.  Diagnostics analysis for log-Birnbaum-Saunders regression models , 2007, Comput. Stat. Data Anal..

[185]  Francisco Cribari-Neto,et al.  Improved statistical inference for the two-parameter Birnbaum-Saunders distribution , 2007, Comput. Stat. Data Anal..

[186]  Steven G. From,et al.  Estimation of the Parameters of the Birnbaum–Saunders Distribution , 2006 .

[187]  W. J. Padgett,et al.  A general class of cumulative damage models for materials failure , 2006 .

[188]  William J. Owen,et al.  A New Three-Parameter Extension to the Birnbaum-Saunders Distribution , 2006, IEEE Transactions on Reliability.

[189]  S. Saunders.  Cumulative Damage Models , 2006 .

[190]  Filidor Vilca-Labra,et al.  A New Fatigue Life Model Based on the Family of Skew-Elliptical Distributions , 2006 .

[191]  Zhihui Wang,et al.  Modified censored moment estimation for the two-parameter Birnbaum-Saunders distribution , 2006, Comput. Stat. Data Anal..

[192]  Wang,et al.  Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Multiply Type-II Censoring , 2006 .

[193]  Antonio Narro,et al.  Some generalisations of Birnbaum-Saunders and sinh-normal distributions , 2006 .

[194]  Debasis Kundu,et al.  Point and interval estimation for the two-parameter Birnbaum-Saunders distribution based on Type-II censored samples , 2006, Comput. Stat. Data Anal..

[195]  Tzong-Ru Tsai,et al.  Acceptance sampling plans for birnbaum-saunders distribution under truncated life tests , 2005 .

[196]  H. Joe.  Asymptotic efficiency of the two-stage estimation method for copula-based models , 2005 .

[197]  José A. Díaz-García,et al.  A new family of life distributions based on the elliptically contoured distributions , 2005 .

[198]  F. Quintana,et al.  Statistical inference for a general class of asymmetric distributions , 2005 .

[199]  Ayman Baklizi,et al.  Acceptance Sampling Based on Truncated Life Tests in the Birnbaum Saunders Model , 2004, Risk analysis : an official publication of the Society for Risk Analysis.

[200]  Jianrong Wu,et al.  Improved interval estimation for the two-parameter Birnbaum-Saunders distribution , 2004, Comput. Stat. Data Anal..

[201]  Gilberto A. Paula,et al.  Influence Diagnostics in log-Birnbaum-Saunders Regression Models , 2004 .

[202]  Fei He-liang.  Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Type-II Bilateral Censoring and Multiply Type-II Censoring , 2004 .

[203]  WANGRong-hua,et al.  Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Type-II Bilateral Censoring and Multiply Type-II Censoring , 2004 .

[204]  Debasis Kundu,et al.  Modified moment estimation for the two-parameter Birnbaum-Saunders distribution , 2003, Comput. Stat. Data Anal..

[205]  David E. Booth,et al.  Applied Multivariate Analysis , 2003, Technometrics.

[206]  James R. Rieck,et al.  A Comparison of Two Random Number Generators for the Birnbaum–Saunders Distribution , 2003 .

[207]  Shuen-Lin Jeng,et al.  Inferences for the Fatigue Life Model Based on the Birnbaum–Saunders Distribution , 2003 .

[208]  W. J. Padgett,et al.  Lower confidence bounds for percentiles of weibull and birnbaum-saunders distributions , 2003 .

[209]  Efthymios G. Tsionas,et al.  BAYESIAN INFERENCE IN BIRNBAUM–SAUNDERS REGRESSION , 2001 .

[210]  G. P. Patil,et al.  Weighted distributions , 2001 .

[211]  Arzu Onar,et al.  Accelerated test models with the inverse Gaussian distribution , 2000 .

[212]  N. Balakrishnan,et al.  Progressive Censoring: Theory, Methods, and Applications , 2000 .

[213]  William J. Padgett,et al.  A Birnbaum-Saunders accelerated life model , 2000, IEEE Trans. Reliab..

[214]  I. N. Volodin,et al.  On limit distributions emerging in the generalized Birnbaum-Saunders model , 2000 .

[215]  G. S. Mudholkar,et al.  The epsilon-skew-normal distribution for analyzing near-normal data , 2000 .

[216]  W. J. Padgett,et al.  Accelerated Test Models for System Strength Based on Birnbaum-Saunders Distributions , 1999, Lifetime data analysis.

[217]  Nancy Reid,et al.  A simple general formula for tail probabilities for frequentist and Bayesian inference , 1999 .

[218]  James R. Rieck,et al.  A moment-generating function with application to the birnbaum-saunders distribution , 1999 .

[219]  W. J. Padgett,et al.  BIRNBAUM-SAUNDERS-TYPE MODELS FOR SYSTEM STRENGTH ASSUMING MULTIPLICATIVE DAMAGE , 1998 .

[220]  D. Dupuis,et al.  Robust estimation of the Birnbaum-Saunders distribution , 1998 .

[221]  Estimation of critical points in the mixture inverse Gaussian model , 1997 .

[222]  Ming-Che Lu,et al.  Bootstrap prediction intervals for the Birnbaum-Saunders distribution , 1997 .

[223]  Ramesh C. Gupta,et al.  On the reliability studies of a weighted inverse Gaussian model , 1995 .

[224]  Abdul L. Bello,et al.  Tables of Integrals, Series, and Products , 1995 .

[225]  A. Desmond,et al.  Shortest prediction intervals for the birnbaum-saunders distribution , 1995 .

[226]  James R. Rieck,et al.  Parameter estimation for ihe birnbaum-saunders distribution based on symmetrically censored samples , 1995 .

[227]  L. Tang,et al.  Random number generator for the Birnbaum-Saunders distribution , 1994 .

[228]  V. Seshadri.  Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods (Ali H. Nayfeh and Balakumar Balachandran) , 2022 .

[229]  Loon Ching Tang,et al.  Percentile bounds and tolerance limits for the birnbaum-saunders distribution , 1994 .

[230]  Loon Ching Tang,et al.  Graphical analysis for Birnbaum-Saunders distribution , 1994 .

[231]  Dong Shang Chang,et al.  Reliability bounds and critical time for the Birnbaum-Saunders distribution , 1993 .

[232]  Jorge Alberto Achcar.  Inferences for the Birnbaum-Saunders fatigue life model using Bayesian methods , 1993 .

[233]  A. Basu,et al.  The Inverse Gaussian Distribution , 1993 .

[234]  P. Sen,et al.  Order statistics and inference : estimation methods , 1992 .

[235]  O. Barndorff-Nielsen.  Modified signed log likelihood ratio , 1991 .

[236]  James R. Rieck,et al.  A log-linear model for the Birnbaum-Saunders distribution , 1991 .

[237]  B. Jørgensen,et al.  On the mixture of the inverse Gaussian distribution with its complementary reciprocal , 1991 .

[238]  K. Fang,et al.  Generalized Multivariate Analysis , 1990 .

[239]  Ramesh C. Gupta,et al.  The role of weighted distributions in stochastic modeling , 1990 .

[240]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .

[241]  O. E. Barndorff-Nielsen,et al.  Infereni on full or partial parameters based on the standardized signed log likelihood ratio , 1986 .

[242]  A. F. Desmond,et al.  On the Relationship between Two Fatigue-Life Models , 1986, IEEE Transactions on Reliability.

[243]  A. Desmond.  Stochastic models of failure in random environments , 1985 .

[244]  Betty Jones Whitten,et al.  Modified Moment Estimation for the Three-Parameter Weibull Distribution , 1984 .

[245]  Arthur Fries,et al.  Fatigue Failure Models ߝ Birnbaum-Saunders vs. Inverse Gaussian , 1982, IEEE Transactions on Reliability.

[246]  W.J. Padgett.  On Bayes Estimation of Reliability for the Birnbaum-Saunders Fatigue Life Model , 1982, IEEE Transactions on Reliability.

[247]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[248]  Lee J. Bain,et al.  Inferences on the Parameters of the Birnbaum-Saunders Fatigue Life Distribution Based on Maximum Likelihood Estimation , 1981 .

[249]  F.J.M. Raaijmakers.  Reliability of Standby System for Units with Birnbaum & Saunders Distribution , 1981, IEEE Transactions on Reliability.

[250]  F. Raaijmakers.  The lifetime of a standby system of units having the Birnbaum and Saunders distribution , 1980, Journal of Applied Probability.

[251]  D. Lindley,et al.  Approximate Bayesian methods , 1980 .

[252]  S J Pocock,et al.  Long-term survival of patients with breast cancer: a study of the curability of the disease. , 1979, British medical journal.

[253]  J. Bernardo.  Reference Posterior Distributions for Bayesian Inference , 1979 .

[254]  N. Draper,et al.  Bayesian Inference on Parameters Associated with Families Closed under Reciprocation. , 1978 .

[255]  N. Singpurwalla,et al.  Methods for Statistical Analysis of Reliability and Life Data. , 1975 .

[256]  Samuel Kotz,et al.  A vector multivariate hazard rate , 1975 .

[257]  F. Hampel.  The Influence Curve and Its Role in Robust Estimation , 1974 .

[258]  E. Kay,et al.  Methods for statistical analysis of reliability and life data , 1974 .

[259]  Sam C. Saunders,et al.  Estimation for a family of life distributions with applications to fatigue , 1969, Journal of Applied Probability.

[260]  Z. Birnbaum,et al.  A new family of life distributions , 1969, Journal of Applied Probability.

[261]  A. Cohen,et al.  Progressively Censored Samples in Life Testing , 1963 .

[262]  M. Shinozuka.  STRUCTURAL SAFETY UNDER CONDITIONS OF ULTIMATE LOAD FAILURE AND FATIGUE , 1961 .

[263]  José A. Díaz-García,et al.  A NEW FAMILY OF LIFE DISTRIBUTIONS BASED ON BIRNBAUM-SAUNDERS DISTRIBUTION , .