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An extension of the generalized Birnbaum-Saunders distribution

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  • Gómez, Héctor W.
  • Olivares-Pacheco, Juan F.
  • Bolfarine, Heleno

Abstract

In this paper we present an extension of the generalized Birnbaum-Saunders distribution family introduced in [Díaz-García, J.A., Leiva-Sánchez, V., 2005. A new family of life distributions based on the contoured elliptically distributions. Journal of Statistical Planning and Inference 128 (2), 445-457] with a view to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied for some special members of this family such as the slash Birnbaum-Saunders and slash-t Birnbaum-Saunders. Simulation studies for some particular cases and a real data analysis are also reported, illustrating the usefulness of the extension considered.

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  • Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:3:p:331-338
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    References listed on IDEAS

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    1. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
    2. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Peter Zörnig, 2019. "On Generalized Slash Distributions: Representation by Hypergeometric Functions," Stats, MDPI, vol. 2(3), pages 1-17, July.
    2. del Castillo, J.M., 2016. "Slash distributions of the sum of independent logistic random variables," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 111-118.
    3. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    4. Dan Xu & Jiaolan He & Zhou Yang, 2022. "Reliability prediction based on Birnbaum–Saunders model and its application to smart meter," Annals of Operations Research, Springer, vol. 312(1), pages 519-532, May.
    5. Lemonte, Artur J. & Cordeiro, Gauss M., 2010. "Asymptotic skewness in Birnbaum-Saunders nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 892-898, May.
    6. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    7. Francisco A. Segovia & Yolanda M. Gómez & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Power Maxwell Distribution with Heavy Tails and Applications," Mathematics, MDPI, vol. 8(7), pages 1-20, July.
    8. Neveka Olmos & Héctor Varela & Héctor Gómez & Heleno Bolfarine, 2012. "An extension of the half-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 875-886, November.
    9. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor W. Gómez, 2017. "The Log-Linear Birnbaum-Saunders Power Model," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 913-933, September.
    10. Gómez, Yolanda M. & Bolfarine, Heleno & Gómez, Héctor W., 2019. "Gumbel distribution with heavy tails and applications to environmental data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 115-129.
    11. 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.
    12. Pilar A. Rivera & Diego I. Gallardo & Osvaldo Venegas & Marcelo Bourguignon & Héctor W. Gómez, 2021. "An Extension of the Truncated-Exponential Skew- Normal Distribution," Mathematics, MDPI, vol. 9(16), pages 1-11, August.
    13. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, February.
    14. Jimmy Reyes & Yuri A. Iriarte, 2023. "A New Family of Modified Slash Distributions with Applications," Mathematics, MDPI, vol. 11(13), pages 1-15, July.
    15. Neveka Olmos & Héctor Varela & Heleno Bolfarine & Héctor Gómez, 2014. "An extension of the generalized half-normal distribution," Statistical Papers, Springer, vol. 55(4), pages 967-981, November.
    16. Filidor Vilca & Camila Borelli Zeller & Gauss M. Cordeiro, 2015. "The sinh-normal/independent nonlinear regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1659-1676, August.
    17. Byun, Manhee & Choe, Changgwon & Cheon, Seunghyun & Lee, Aejin & Lim, Hankwon, 2022. "Statistical and stochastic feasibility studies of potential liquid organic hydrogen carriers in a membrane reactor for simultaneous hydrogen storage and production: Technical, economic, and environmen," Renewable Energy, Elsevier, vol. 195(C), pages 1393-1411.
    18. Fierro, Raúl & Leiva, Víctor & Ruggeri, Fabrizio & Sanhueza, Antonio, 2013. "On a Birnbaum–Saunders distribution arising from a non-homogeneous Poisson process," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1233-1239.
    19. Li, Ai-Ping & Xie, Feng-Chang, 2012. "Diagnostics for a class of survival regression models with heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4204-4214.

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