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The beta generalized Rayleigh distribution with applications to lifetime data

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  • Gauss Cordeiro
  • Cláudio Cristino
  • Elizabeth Hashimoto
  • Edwin Ortega

Abstract

For the first time, we propose a new distribution so-called the beta generalized Rayleigh distribution that contains as special sub-models some well-known distributions. Expansions for the cumulative distribution and density functions are derived. We obtain explicit expressions for the moments, moment generating function, mean deviations, Bonferroni and Lorenz curves and densities of the order statistics and their moments. We estimate the parameters by maximum likelihood and provide the observed information matrix. The usefulness of the new distribution is illustrated through two real data sets that show that it is quite flexible in analyzing positive data instead of the generalized Rayleigh and Rayleigh distributions. Copyright Springer-Verlag 2013

Suggested Citation

  • Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:1:p:133-161
    DOI: 10.1007/s00362-011-0415-0
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    References listed on IDEAS

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    1. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    2. Fathi Manesh, Sirous & Khaledi, Baha-Eldin, 2008. "On the likelihood ratio order for convolutions of independent generalized Rayleigh random variables," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3139-3144, December.
    3. Tzong-Ru Tsai & Shuo-Jye Wu, 2006. "Acceptance sampling based on truncated life tests for generalized Rayleigh distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(6), pages 595-600.
    4. Kundu, Debasis & Raqab, Mohammad Z., 2005. "Generalized Rayleigh distribution: different methods of estimations," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 187-200, April.
    5. Felipe Gusmão & Edwin Ortega & Gauss Cordeiro, 2011. "The generalized inverse Weibull distribution," Statistical Papers, Springer, vol. 52(3), pages 591-619, August.
    6. Pescim, Rodrigo R. & Demétrio, Clarice G.B. & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Urbano, Mariana R., 2010. "The beta generalized half-normal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 945-957, April.
    7. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    8. Koutrouvelis, Ioannis A. & Canavos, George C. & Meintanis, Simos G., 2005. "Estimation in the three-parameter inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1132-1147, June.
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    Cited by:

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    3. Hanan Haj Ahmad & Dina A. Ramadan & Ehab M. Almetwally, 2024. "Evaluating the Discrete Generalized Rayleigh Distribution: Statistical Inferences and Applications to Real Data Analysis," Mathematics, MDPI, vol. 12(2), pages 1-23, January.
    4. Karol I. Santoro & Diego I. Gallardo & Osvaldo Venegas & Isaac E. Cortés & Héctor W. Gómez, 2023. "A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    5. Ingo Hoffmann & Christoph J. Börner, 2021. "The risk function of the goodness-of-fit tests for tail models," Statistical Papers, Springer, vol. 62(4), pages 1853-1869, August.
    6. Domma, Filippo & Condino, Francesca, 2014. "A new class of distribution functions for lifetime data," Reliability Engineering and System Safety, Elsevier, vol. 129(C), pages 36-45.
    7. Jose K. K. & Sivadas Remya, 2015. "Negative Binomial Marshall–Olkin Rayleigh Distribution and Its Applications," Stochastics and Quality Control, De Gruyter, vol. 30(2), pages 89-98, December.

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