Journal of Statistical Theory and Practice

, Volume 8, Issue 2, pp 283–296 | Cite as

A Generalization of the Slash Half Normal Distribution: Properties and Inferences

  • Wenhao GuiEmail author


In this article, we introduce a generalization of the slash half normal distribution. We define the generalization by means of a stochastic representation as the mixture of a generalized half normal random variable with respect to a power of a uniform random variable. The proposed generalization is more flexible in terms of its kurtosis than the slash half normal distribution. Properties involving moments are studied. We apply the distribution to some data applications where model fitting is implemented by a maximum likelihood procedure.


Half normal distribution Slash distribution Kurtosis Skewness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arslan, O. 2008. An alternative multivariate skew-slash distribution. Stat. Prob. Lett., 78(16), 2756–2761.MathSciNetCrossRefGoogle Scholar
  2. Arslan, O. 2009. Maximum likelihood parameter estimation for the multivariate skew-slash distribution. Stat. Prob. Lett., 79(20), 2158–2165.MathSciNetCrossRefGoogle Scholar
  3. Arslan, O. and A. İ. Genç. 2009. A generalization of the multivariate slash distribution. J. Stat. Plan. Inference, 139(3), 1164–1170.MathSciNetCrossRefGoogle Scholar
  4. Atkinson, A. C. 1985. Plots, transformations, and regression: An introduction to graphical methods of diagnostic regression analysis. Oxford, UK: Clarendon Press.zbMATHGoogle Scholar
  5. Azzalini, A. 1985. A class of distributions which includes the normal ones. Scand. J. Stat., 12(2), 171–178.MathSciNetzbMATHGoogle Scholar
  6. Azzalini, A., and A. Capitanio. 2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J. R. Stat. Soc. Ser. B Stat. Methodol., 65(2), 367–389.MathSciNetCrossRefGoogle Scholar
  7. Bolfarine, H., H. W. Gómez, and L. I. Rivas. 2011. The log-bimodal-skew-normal model. a geochemical application. J. Chemometrics, 25(6), 329–332.CrossRefGoogle Scholar
  8. DiCiccio, T. J. 1987. Approximate inference for the generalized gamma distribution. Technometrics, 29(1), 33–40.MathSciNetCrossRefGoogle Scholar
  9. da Silva Ferreira, C., H. Bolfarine, and V. H. Lachos. 2011. Skew scale mixtures of normal distributions: Properties and estimation. Stat. Methodol., 8(2), 154–171.MathSciNetCrossRefGoogle Scholar
  10. Ferrari, S., and F. Cribari-Neto. 2004. Beta regression for modelling rates and proportions. J. Appl. Stat., 31(7), 799–815.MathSciNetCrossRefGoogle Scholar
  11. Gómez, H. W., F. A. Quintana, and F. J. Torres. 2007. A new family of slash-distributions with elliptical contours. Stat. Prob. Lett., 77(7), 717–725.MathSciNetCrossRefGoogle Scholar
  12. Gómez, H. W., F. J. Torres, and H. Bolfarine. 2007. Large-sample inference for the epsilon-skew-t distribution. Communications in Statistics Theory and Methods, 36(1), 73–81.MathSciNetCrossRefGoogle Scholar
  13. Gómez, H. W., O. Venegas, and H. Bolfarine. 2007. Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics, 18(4), 395–407.MathSciNetCrossRefGoogle Scholar
  14. Hager, H. W., and L. J. Bain. 1970. Inferential procedures for the generalized gamma distribution. J. Am. Stat. Assoc., 65(332), 1601–1609.CrossRefGoogle Scholar
  15. Jamshidian, M. 2001. A note on parameter and standard error estimation in adaptive robust regression. J. Stat. Comput. Simulation, 71(1), 11–27.MathSciNetCrossRefGoogle Scholar
  16. Johnson, N. L., S. Kotz, and N. Balakrishnan. 1995. Continuous univariate distributions, Vol. 2 of PWiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. New York, NY: Wiley.zbMATHGoogle Scholar
  17. Kafadar, K. 1982. A biweight approach to the one-sample problem. J. Am. Stat. Assoc., 77(378), 416–424.CrossRefGoogle Scholar
  18. Kashid, D. N. and S. R. Kulkarni. 2003. Subset selection in multiple linear regression with heavy tailed error distribution. J. Stat. Comput. Simulation, 73(11), 791–805.MathSciNetCrossRefGoogle Scholar
  19. Lawless, J. 1980. Inference in the generalized gamma and log gamma distributions. Technometrics, 22(3), 409–419.MathSciNetCrossRefGoogle Scholar
  20. Morgenthaler, S. 1986. Robust confidence intervals for a location parameter: The configural approach. J. Am. Stat. Assoc., 81(394), 518–525.MathSciNetCrossRefGoogle Scholar
  21. Mosteller, F., and J. W. Tukey. 1977. Data analysis and regression. A second course in statistics. Addison-Wesley Series in Behavioral Science: Quantitative Methods. Reading, MA: Addison-Wesley.Google Scholar
  22. Olmos, N. M., H. Varela, H. W. Gómez, and H. Bolfarine. 2012. An extension of the half-normal distribution. Stat. Papers, 53(4), 875–886.MathSciNetCrossRefGoogle Scholar
  23. Parr, V. B., and J. T. Webster. 1965. A method for discriminating between failure density functions used in reliability predictions. Technometrics, 7(1), 1–10.CrossRefGoogle Scholar
  24. Pewsey, A. 2002. Large-sample inference for the general half-normal distribution. Commun. Stat. Theory Methods, 31(7), 1045–1054.MathSciNetCrossRefGoogle Scholar
  25. Pewsey, A. 2004. Improved likelihood based inference for the general half-normal distribution. Communi. Stat. Theory Methods, 33(2), 197–204.MathSciNetCrossRefGoogle Scholar
  26. Rogers, W. H., and J. W. Tukey. 1972. Understanding some long-tailed symmetrical distributions. Stat. Neerland., 26(3), 211–226.MathSciNetCrossRefGoogle Scholar
  27. Stacy, E.W. 1962. A generalization of the gamma distribution. Ann. of Math. Stat., 33(3), 1187–1192.MathSciNetCrossRefGoogle Scholar
  28. Stacy, E. W. and Mihram, G. A. 1965. Parameter estimation for a generalized gamma distribution. Technometrics, 7(3), 349–358.MathSciNetCrossRefGoogle Scholar
  29. Wang, J., and M. G. Genton. 2006. The multivariate skew-slash distribution. J. Stat. Plan. Inference, 136(1), 209–220.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of MinnesotaDuluthUSA

Personalised recommendations