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A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications

Author

Listed:
  • Gauss Moutinho Cordeiro

    (Departamento de Estatística, Universidade Federal de Pernambuco, Recife 50740-540, Brazil)

  • Maria Do Carmo Soares De Lima

    (Departamento de Estatística, Universidade Federal de Pernambuco, Recife 50740-540, Brazil)

  • Edwin Moisés Marcos Ortega

    (Departamento de Ciências Exatas, Universidade de São Paulo, São Paulo 13418-900, Brazil)

  • Adriano Kamimura Suzuki

    (Departamento de Matemática Aplicada e Estatística, Universidade de São Paulo, São Paulo 13566-590, Brazil)

Abstract

We propose an extended fatigue lifetime model called the odd log-logistic Birnbaum–Saunders–Poisson distribution, which includes as special cases the Birnbaum–Saunders and odd log-logistic Birnbaum–Saunders distributions. We obtain some structural properties of the new distribution. We define a new extended regression model based on the logarithm of the odd log-logistic Birnbaum–Saunders–Poisson random variable. For censored data, we estimate the parameters of the regression model using maximum likelihood. We investigate the accuracy of the maximum likelihood estimates using Monte Carlo simulations. The importance of the proposed models, when compared to existing models, is illustrated by means of two real data sets.

Suggested Citation

  • Gauss Moutinho Cordeiro & Maria Do Carmo Soares De Lima & Edwin Moisés Marcos Ortega & Adriano Kamimura Suzuki, 2018. "A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications," Stats, MDPI, vol. 1(1), pages 1-16, May.
    • Handle: RePEc:gam:jstats:v:1:y:2018:i:1:p:4-47:d:147763
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    References listed on IDEAS

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    1. Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The [beta]-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1445-1461, March.
    2. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    3. Altemir Silva Braga & Gauss M. Cordeiro & Edwin M. M. Ortega & Giovana O. Silva, 2017. "The Odd Log-Logistic Student t Distribution: Theory and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 615-639, December.
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    Cited by:

    1. Lucas D. Ribeiro Reis & Gauss M. Cordeiro & Maria do Carmo S. Lima, 2022. "The Stacy-G Class: A New Family of Distributions with Regression Modeling and Applications to Survival Real Data," Stats, MDPI, vol. 5(1), pages 1-43, March.

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