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Bimodal Birnbaum–Saunders distribution with applications to non negative measurements

Author

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  • Neveka M. Olmos
  • Guillermo Martínez-Flórez
  • Heleno Bolfarine

Abstract

In this article, we introduce a new extension of the Birnbaum–Saunders (BS) distribution as a follow-up to the family of skew-flexible-normal distributions. This extension produces a family of BS distributions including densities that can be unimodal as well as bimodal. This flexibility is important in dealing with positive bimodal data, given the difficulties experienced by the use of mixtures of distributions. Some basic properties of the new distribution are studied including moments. Parameter estimation is approached by the method of moments and also by maximum likelihood, including a derivation of the Fisher information matrix. Three real data illustrations indicate satisfactory performance of the proposed model.

Suggested Citation

  • Neveka M. Olmos & Guillermo Martínez-Flórez & Heleno Bolfarine, 2017. "Bimodal Birnbaum–Saunders distribution with applications to non negative measurements," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6240-6257, July.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:13:p:6240-6257
    DOI: 10.1080/03610926.2015.1133824
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    Cited by:

    1. Guillermo Martínez-Flórez & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2021. "Flexible Log-Linear Birnbaum–Saunders Model," Mathematics, MDPI, vol. 9(11), pages 1-23, May.
    2. Guillermo Martínez-Flórez & David Elal-Olivero & Carlos Barrera-Causil, 2021. "Extended Generalized Sinh-Normal Distribution," Mathematics, MDPI, vol. 9(21), pages 1-24, November.
    3. Jimmy Reyes & Jaime Arrué & Víctor Leiva & Carlos Martin-Barreiro, 2021. "A New Birnbaum–Saunders Distribution and Its Mathematical Features Applied to Bimodal Real-World Data from Environment and Medicine," Mathematics, MDPI, vol. 9(16), pages 1-19, August.

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