Robust estimation of the Birnbaum-Saunders distribution

Dupuis, Debbie J.; Mills, Joanna

doi:10.1109/24.690913

Cited by 60 publications

(27 citation statements)

References 24 publications

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“…Desmond [9] also strengthened the physical justification for the use of this distribution by relaxing the assumptions made originally by Birnbaum and Saunders [4]. Some recent work on the BS distribution can be found in Balakrishnan et al [2], Chang and Tang [7,8], Dupuis and Mills [10], From and Li [11],…”

Section: Introductionmentioning

confidence: 99%

On the hazard function of Birnbaum–Saunders distribution and associated inference

Kundu

Kannan

Balakrishnan

2008

Computational Statistics & Data Analysis

123

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In this paper, we discuss the shape of the hazard function of Birnbaum-Saunders distribution. Specifically, we establish that the hazard function of Birnbaum-Saunders distribution is an upside down function for all values of the shape parameter. In reliability and survival analysis, as it is often of interest to determine the point at which the hazard function reaches its maximum, we propose different estimators of that point and evaluate their performance using Monte Carlo simulations. Next, we analyze a data set and illustrate all the inferential methods developed here and finally make some concluding remarks.

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Section: Introductionmentioning

confidence: 99%

On the hazard function of Birnbaum–Saunders distribution and associated inference

Kundu

Kannan

Balakrishnan

2008

Computational Statistics & Data Analysis

123

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“…Accordingly, it becomes necessary to investigate the performance of the estimators under a scenario in which data are contaminated with outliers. In a similar way as done by (Dupuis and Mills 1998), we compare the performances of the proposed estimators and that of the MLEs based on the following four possible models. The reference distribution is the BS distribution with the parameters α = 0.5 and β = 1.…”

Section: Numerical Results With Contaminationmentioning

confidence: 99%

“…To evaluate robustness of the proposed methods, we follow the same scenario by Dupuis and Mills (1998) and assume that the 51st observation t 51 was misrecorded as 633, instead of 133. It is desirable that the estimated shape and scale parameters should be very similar under the two scenarios, because we already know that the observation t 51 is a recording error.…”

Section: An Illustrative Examplementioning

confidence: 99%

“…It deserves mentioning that Dupuis and Mills (1998) developed the robust estimation procedures based on an optimal bias-robust estimator (OBRE) of the BS distribution, whereas the OBRE is not in explicit form and it may suffer from the problem of convergence. These observations give rise to the need for some alternative estimators, which should be easy to calculate for practitioners and are also quite robust against a certain amount of data contamination.…”

Section: Introductionmentioning

confidence: 99%

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Simple robust parameter estimation for the Birnbaum-Saunders distribution

2015

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We study the problem of robust estimation for the two-parameter Birnbaum-Saunders distribution. It is well known that the maximum likelihood estimator (MLE) is efficient when the underlying model is true but at the same time it is quite sensitive to data contamination that is often encountered in practice. In this paper, we propose several estimators which have simple closed forms and are also robust to data contamination. We study the breakdown points and asymptotic properties of the proposed estimators. These estimators are then applied to both simulated and real datasets. Numerical results show that the proposed estimators are attractive alternative to the MLE in that they are quite robust to data contamination and also highly efficient when the underlying model is true.

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“…The initial period contains few published papers reflecting the slow development of the methodology; see, for example, Birnbaum and Saunders (1969a); Rieck and Nedelman (1991); Johnson et al (1995); Dupuis and Mills (1998) and Owen and Padgett (1999). The second period (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010) includes papers that discuss varied aspects of estimation, modelling and diagnostics, as well as generalizations, computational issues and novel modelling examples, but with justifications still mainly based on an argument of cumulative effects; see, for example, Owen and Padgett (2000); Volodin and Dzhungurova (2000); Tsionas (2001); Rieck (2003); Galea et al (2004); Owen (2006); Xie and Wei (2007); Lemonte et al (2008); Leiva et al (2008Leiva et al ( , 2009); Balakrishnan et al (2009) and Vilca et al (2010).…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

Aykroyd

Leiva

Marchant

2018

Risks

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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.

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Robust estimation of the Birnbaum-Saunders distribution

Cited by 60 publications

References 24 publications

On the hazard function of Birnbaum–Saunders distribution and associated inference

On the hazard function of Birnbaum–Saunders distribution and associated inference

Simple robust parameter estimation for the Birnbaum-Saunders distribution

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

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