Skip to main content
SpringerLink
Log in

The Log-Linear Birnbaum-Saunders Power Model

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

Abstract

In this paper the sinh-power model is developed as a natural follow up to the log-linear Birnbaum-Saunders power model. The class of models resulting, incorporates the sinh-power-normal model, the ordinary sinh-normal model and the log-linear Birnbaum-Saunders model (Rieck and Nedelman, Technometrics 33:51–60, 1991). Maximum likelihood estimation is developed with the Hessian matrix used for standard error estimation. An application is reported for the data set on lung cancer studied in Kalbfleisch and Prentice (2002), where it is shown that the log-linear Birnbaum-Saunders power-normal model presents better fit than the log-linear Birnbaum-Saunders model. Another application is devoted to a fatigue data set previously analyzed in the literature. A nonlinear Birnbaum-Saunders power-normal model is fitted to the data set, with satisfactory performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Akaike H (1974) A new look at statistical model identification. IEEE Transaction on Automatic Control 19:716–723

    Article  MathSciNet  MATH  Google Scholar 

  • Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Stat 12:171–178

    MathSciNet  MATH  Google Scholar 

  • Barros M, Paula G A, Leiva V (2008) A new class of survival regression models with heavy-tailed errors: robustness and diagnostics. Lifetime Data Anal 14:316–332

    Article  MathSciNet  MATH  Google Scholar 

  • Birnbaum Z W, Saunders S C (1969) A new family of life distributions. J Appl Probab 6:319–327

    Article  MathSciNet  MATH  Google Scholar 

  • Castillo N, Gómez HW, Bolfarine H (2011) Epsilon Birnbaum-Saunders distribution family: properties and inference. Stat Pap 52:871–883

    Article  MathSciNet  MATH  Google Scholar 

  • Cox D R, Hinkley DV (1974) Theorical statistics. Chapman and Hall, London

    Book  MATH  Google Scholar 

  • Díaz-García JA, Leiva-Sánchez V (2005) A new family of life distributions based on the elliptically contoured distributions. J Statist Plann Inference 128:445–457

    Article  MathSciNet  MATH  Google Scholar 

  • Durrans S R (1992) Distributions of fractional order statistics in hydrology. Water Resour Res 28:1649–1655

    Article  Google Scholar 

  • Galea M, Leiva V, Paula G (2004) Influence diagnostics in log-Birnbaum-Saunders regression models. J Appl Stat 31:1049–1064

    Article  MathSciNet  MATH  Google Scholar 

  • Gómez HW, Olivares J, Bolfarine H (2009) An extension of the generalized Birnbaum-Saunders distribution. Statistics and Probability Letters 79:331–338

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta D, Gupta R C (2008) Analyzing skewed data by power normal model. Test 17:197–210

    Article  MathSciNet  MATH  Google Scholar 

  • Jones M C, Pewsey A (2009) Sinh-arcsinh distributions. Biometrika 96 (4):761–780

    Article  MathSciNet  MATH  Google Scholar 

  • Kalbfleisch J D, Prentice R L (2002) The statistical analysis of faiture time data. Wiley, New York

    Book  MATH  Google Scholar 

  • Kullback S, Leibler R A (1951) On information and sufficiency. Ann Math Stat 22:79–86

    Article  MathSciNet  MATH  Google Scholar 

  • Lachos V H, Bolfarine H, Arellano-Valle R B, Montenegro L C (2007) Likelihood-based inference for multivariate skew-normal regression models. Communications in Statistics-Theory and Methods 36:1769–1786

    Article  MathSciNet  MATH  Google Scholar 

  • Lee E T, Wang J W (2003) Statistical methods for survival data analysis. John Wiley, NY

    Book  MATH  Google Scholar 

  • Lehmann E L (1953) The power of rank tests. Ann Math Stat 24:23–43

    Article  MathSciNet  MATH  Google Scholar 

  • Leiva V, Vilca F, Balakrishnan N, Sanhueza A (2010) A skewed Sinh-Normal distribution and its properties and application to air pollution. Communications in Statistics Theory and Methods 39:426–443

    Article  MathSciNet  MATH  Google Scholar 

  • Lemonte A J (2012) A log-Birnbaum-Saunders regression model with asymmetric errors. J Stat Comput Simul 84:1775–1787

    Article  MathSciNet  MATH  Google Scholar 

  • Martínez-Flórez G, Bolfarine H, Gómez HW (2014) An alpha-power extension for the Birnbaum-Saunders distribution. Statistics: A Journal of Theoretical and Applied Statistics 48(5):971–982

    Article  MathSciNet  MATH  Google Scholar 

  • Ortega E M M, Paula G A, Bolfarine H (2008) Deviance residuals in generalised log-gamma regression models with censored observations. J Stat Comput Simul 78 (8):747–764

    Article  MathSciNet  MATH  Google Scholar 

  • Pewsey A, Gómez HW, Bolfarine H (2012) Likelihood-based inference for power distributions. Test 21:775–789

    Article  MathSciNet  MATH  Google Scholar 

  • Rieck J R, Nedelman J R (1991) A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33:51–60

    MATH  Google Scholar 

  • Santana L, Vilca F, Leiva V (2011) Influence analysis in skew-Birnbaum-Saunders regression models and applications. J Appl Stat 38:1633–1649

    Article  MathSciNet  MATH  Google Scholar 

  • Therneau T M, Grambsch P M, Fleming T R (1990) Martingale-based residuals for survival models. Biometrika 77:147–160

    Article  MathSciNet  MATH  Google Scholar 

  • Vilca-Labra F, Leiva-Sanchez V (2006) A new fatigue life model based on the family of skew-elliptical distributions. Communications in Statistics-Theory and Methods 35:229–244

    Article  MathSciNet  MATH  Google Scholar 

  • Vuong Q (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57:307–333

    Article  MathSciNet  MATH  Google Scholar 

  • Wei B C, Hu Y Q, Fung W K (1998) Generalized leverage and its applications. Scand J Statist 25:25–37

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Córdoba, Colombia

    Guillermo Martínez-Flórez

  2. Departamento de Estatítica, IME, Universidade de São Paulo, São Paulo, Brazil

    Heleno Bolfarine

  3. Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile

    Héctor W. Gómez

Authors
  1. Guillermo Martínez-Flórez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heleno Bolfarine
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Héctor W. Gómez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Héctor W. Gómez.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Martínez-Flórez, G., Bolfarine, H. & Gómez, H.W. The Log-Linear Birnbaum-Saunders Power Model. Methodol Comput Appl Probab 19, 913–933 (2017). https://doi.org/10.1007/s11009-016-9526-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11009-016-9526-3

Keywords

Mathematics Subject Classification (2010)

Search

Navigation