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The beta generalized half-normal distribution

Author

Listed:
  • Pescim, Rodrigo R.
  • Demétrio, Clarice G.B.
  • Cordeiro, Gauss M.
  • Ortega, Edwin M.M.
  • Urbano, Mariana R.

Abstract

For the first time, we propose the so-called beta generalized half-normal distribution, which contains some important distributions as special cases, such as the half-normal and generalized half-normal (Cooray and Ananda, 2008) distributions. We derive expansions for the cumulative distribution and density functions which do not depend on complicated functions. We obtain formal expressions for the moments of the new distribution. We examine the maximum likelihood estimation of the parameters and provide the expected information matrix. The usefulness of the new distribution is illustrated through a real data set by showing that it is quite flexible in analyzing positive data instead of the generalized half-normal, half-normal, Weibull and beta Weibull distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:4:p:945-957
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    References listed on IDEAS

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    1. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2007. "A flexible Weibull extension," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 719-726.
    2. 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.
    3. Nadarajah, Saralees, 2008. "Explicit expressions for moments of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 196-205, February.
    4. 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.
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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. Cordeiro, Gauss M. & Lemonte, Artur J., 2011. "The beta Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 973-982, August.
    3. Mameli, Valentina, 2015. "The Kumaraswamy skew-normal distribution," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 75-81.
    4. Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.
    5. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    6. Mavis Pararai & Broderick O. Oluyede & Gayan Warahena-Liyanage, 2016. "The Beta Lindley-Poisson Distribution with Applications," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 5(4), pages 1-1.
    7. Mahmoudi, Eisa, 2011. "The beta generalized Pareto distribution with application to lifetime data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2414-2430.
    8. 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.
    9. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2020. "Risk Analysis through the Half-Normal Distribution," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    10. Lamia HASNAOUI & Besma BELHADJ, 2015. "Fuzzy multidimensional inequality measurement. Policies to reduce inequality in Tunisia," EuroEconomica, Danubius University of Galati, issue 2(34), pages 21-28, November.

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