Diagnostics analysis for log-Birnbaum–Saunders regression models

Xie, Fei; Wei, Bo‐Cheng

doi:10.1016/j.csda.2006.08.030

Cited by 72 publications

(47 citation statements)

References 17 publications

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“…Lemonte et al [16], Rieck [23,24], Ng et al [18,19], Owen [20] and Xie and Wei [26]. A concise review of different developments on the BS distribution until 1995 can be found in the book by Johnson et al [14].…”

Section: Introductionmentioning

confidence: 99%

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

Kundu

Kannan

Balakrishnan

2008

Computational Statistics & Data Analysis

120

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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

120

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“…Then the ℎ case could be considered as influential observation if ̂− is far from ̂. This methodology was conducted in many statistical models, see for example, Christensen, Pearson and Johnson [17], Davison and Tsai [18], Xie and Wei [19] and Xie and Wei [20]. The case deletion model for the LF regression model (4) is given by:…”

Section: Sensitivity Analysismentioning

confidence: 99%

Estimation and application in log-FrÃ©chet regression model using censored data

Alamoudi

Mousa

Baharith

2017

IJASP

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This article introduces a new location-scale regression model based on a log-Fréchet distribution. Maximum likelihood and Jackknife methods are used to estimate the new model parameters for censored data. Martingale and deviance residuals are obtained to check model assumptions, data validity, and detect outliers. Moreover, global influence is used to detect influential observations. Monte Carlo simulation study is provided to compare the performance of the maximum likelihood and jackknife estimators for different sample sizes and censoring percentages. The empirical distribution of the martingale and deviance residuals of the proposed model is examined. A real lifetime heart transplant data is analyzed under the log-Fréchet regression model to illustrate the satisfactory results of the proposed model.

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“…651-63) and Leiva (2016, p. 18). In addition, a logarithmic verion of the BS distribution (log-BS) was introduced by Rieck and Nedelman (1991) allowing the extension to BS log-linear regression models; see Tsionas (2001); Galea et al (2004); Xie and Wei (2007); Desmond et al (2008); Lemonte (2011); Ferrari (2011a, 2011b).…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

“…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). The third period (2011 to the present) is characterized by a new inventiveness, breaking the link with lifetime data analysis and hence extended application in new areas such as: biology, crop yield assessment, econometrics, energy production, forestry, industry, informatics, insurance, inventory management, medicine, psychology, neurology, pollution monitoring, quality control, sociology and seismology; see, for example, Bhatti (2010); Kotz et al (2010); Balakrishnan et al (2011); Leiva et al (2010Leiva et al ( , 2011Leiva et al ( , 2012; Vilca et al (2010); Villegas et al (2011); Azevedo et al (2012); Ferreira et al (2012);...…”

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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Diagnostics analysis for log-Birnbaum–Saunders regression models

Cited by 72 publications

References 17 publications

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

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

Estimation and application in log-FrÃ©chet regression model using censored data

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

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