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An extension of the half-normal distribution

Author

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  • Neveka Olmos
  • Héctor Varela
  • Héctor Gómez
  • Heleno Bolfarine

Abstract

In this paper we introduce a new distribution, namely, the slashed half-normal distribution and it can be seen as an extension of the half-normal distribution. It is shown that the resulting distribution has more kurtosis than the ordinary half-normal distribution. Moments and some properties are derived for the new distribution. Moment estimators and maximum likelihood estimators can computed using numerical procedures. Results of two real data application are reported where model fitting is implemented by using maximum likelihood estimation. The applications illustrate the better performance of the new distribution. Copyright Springer-Verlag 2012

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  • 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.
    • Handle: RePEc:spr:stpapr:v:53:y:2012:i:4:p:875-886
    DOI: 10.1007/s00362-011-0391-4
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    References listed on IDEAS

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    1. Arslan, Olcay, 2009. "Maximum likelihood parameter estimation for the multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2158-2165, October.
    2. Arslan, Olcay, 2008. "An alternative multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2756-2761, November.
    3. 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.
    4. 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.
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    Cited by:

    1. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas & Héctor W. Gómez, 2024. "A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data," Mathematics, MDPI, vol. 12(11), pages 1-17, May.
    2. Mastrantonio, Gianluca, 2018. "The joint projected normal and skew-normal: A distribution for poly-cylindrical data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 14-26.
    3. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas, 2022. "The Heavy-Tailed Gleser Model: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    4. Jimmy Reyes & Yuri A. Iriarte & Pedro Jodrá & Héctor W. Gómez, 2019. "The Slash Lindley-Weibull Distribution," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 235-251, March.
    5. Juan M. Astorga & Jimmy Reyes & Karol I. Santoro & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function," Mathematics, MDPI, vol. 8(9), pages 1-12, September.
    6. 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.
    7. 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.
    8. Yolanda M. Gómez & Luis Firinguetti-Limone & Diego I. Gallardo & Héctor W. Gómez, 2023. "An Extension of the Akash Distribution: Properties, Inference and Application," Mathematics, MDPI, vol. 12(1), pages 1-15, December.
    9. Diego I. Gallardo & Yolanda M. Gómez & Héctor J. Gómez & María José Gallardo-Nelson & Marcelo Bourguignon, 2023. "The Slash Half-Normal Distribution Applied to a Cure Rate Model with Application to Bone Marrow Transplantation," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    10. Héctor J. Gómez & Karol I. Santoro & Inmaculada Barranco-Chamorro & Osvaldo Venegas & Diego I. Gallardo & Héctor W. Gómez, 2023. "A Family of Truncated Positive Distributions," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    11. Talha Arslan, 2021. "An α -Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    12. 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.
    13. Leonardo Barrios & Yolanda M. Gómez & Osvaldo Venegas & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2022. "The Slashed Power Half-Normal Distribution with Applications," Mathematics, MDPI, vol. 10(9), pages 1-21, May.

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