A new family of life distributions based on the elliptically contoured distributions

Dı́az-Garcı́a, José A.; Leiva, Víctor

doi:10.1016/j.jspi.2003.11.007

Cited by 147 publications

(60 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The BS distribution has been generalized to obtain a major degree of flexibility essentially in the kurtosis; see [3,23,24]. Two particular cases of generalized BS (GBS) distributions are the classic BS distribution and the one generated from the Student-t (or simply t) model, known as the BS-t distribution.…”

Section: Introductionmentioning

confidence: 99%

Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance

Paula

Leiva

Barros

et al. 2011

Appl Stoch Models Bus & Ind

102

View full text Add to dashboard Cite

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model.

show abstract

Section: Introductionmentioning

confidence: 99%

Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance

Paula

Leiva

Barros

et al. 2011

Appl Stoch Models Bus & Ind

102

View full text Add to dashboard Cite

show abstract

“…> D e > ijN representing an N 1 vector that has an one at the ij th position, and zeros in the other positions. If (15) is derived with respect to Â D OE˛; ; Á > , we obtain the perturbation matrix given in (A.3) of Appendix A.…”

Section: Local Influencementioning

confidence: 99%

“…651-658] and [2]. Several generalizations and extensions of the BS distribution have been made by [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Implementations in the R software of BS distributions can be found in [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Diagnostics in Birnbaum–Saunders accelerated life models with an application to fatigue data

Leiva

Rojas

Galea

et al. 2012

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

In industrial statistics, there is great interest in predicting with precision lifetimes of specimens that operate under stress. For example, a bad estimation of the lower percentiles of a life distribution can produce significant monetary losses to organizations due to an excessive amount of warranty claims. The Birnbaum–Saunders distribution is useful for modeling lifetime data. This is because such a distribution allows us to relate the total time until the failure occurs to some type of cumulative damage produced by stress. In this paper, we propose a methodology for detecting influence of atypical data in accelerated life models on the basis of the Birnbaum–Saunders distribution. The methodology developed in this study should be considered in the design of structures and in the prediction of warranty claims. We conclude this work with an application of the proposed methodology on the basis of real fatigue life data, which illustrates its importance in a warranty claim problem. Copyright © 2012 John Wiley & Sons, Ltd.

show abstract

“…The BS distribution has received significant attention over the last few years by many researchers such as Wu and Wong (2004), Kundu et al (2008), Lemonte et al (2007Lemonte et al ( , 2008, Xu and Tang (2010) and Bhatti (2010), among others. Some generalizations and extensions of the BS distribution are proposed in Díaz- García and Leiva (2005), Owen (2006), Vilca and Leiva (2006), Gómes et al (2009), Guiraud et al (2009), Leiva et al (2010 and Cordeiro and Lemonte (2011). In this study, a new three-parameter extension for the BS distribution is proposed.…”

Section: Introductionmentioning

confidence: 99%

A new extension of the Birnbaum–Saunders distribution

Lemonte¹

2013

Braz. J. Probab. Stat.

View full text Add to dashboard Cite

In this paper, a new extension for the Birnbaum-Saunders distribution, which has been applied to the modeling of fatigue failure times and reliability studies, is introduced. The proposed model, called the Marshall-Olkin extended Birnbaum-Saunders distribution, arises based on the scheme introduced by Marshall and Olkin [Biometrika 84 (1997) 641-652]. The maximum likelihood estimators and statistical inference for the new distribution parameters and influence diagnostic for the new distribution are presented. Finally, the proposed new distribution is applied to model three real data sets.

show abstract

A new family of life distributions based on the elliptically contoured distributions

Cited by 147 publications

References 11 publications

Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance

Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance

Diagnostics in Birnbaum–Saunders accelerated life models with an application to fatigue data

A new extension of the Birnbaum–Saunders distribution

Contact Info

Product

Resources

About