On the skewed sinh-normal distribution

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    Leiva et al. [10] introduce the skewed sinh-normal distribution, which is a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum–Saunders distribution associated with this distribution. In this paper, we will introduce further properties of the skewed sinh-normal distribution, and introduce a new approximate form of its probability density function and cumulative distribution function (cdf), along with numerical comparison between the exact and approximate values of its cdf. Moreover, a random number generator for the distribution will be suggested and a goodness of fit test will be carried out to examine the effectiveness of the proposed random number generator. Finally, maximum likelihood estimation for the unknown parameter of the skewed sinh-normal distribution will be investigated, and numerical illustration for the new results will be discussed.


  • Keywords


    Skew Distributions; Approximation; Random Number Generator; Maximum Likelihood Estimation.

  • References


      [1] Ashour, S.K., Abdel-hameed, M.A. (2010). Approximate skew normal distribution. Journal of Advanced Research 1:341–350. http://dx.doi.org/10.1016/j.jare.2010.06.004.

      [2] Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12:171–178.

      [3] Birnbaum, Z.W., Saunders, S.C. (1969). A new family of life distributions. Journal of Applied probability 6:319–327. http://dx.doi.org/10.2307/3212003.

      [4] Galea, M., Leiva, V., Paula, G. A. (2004). Influence diagnostics in log Birnbaum–Saunders regression models. Journal of Applied Statistics 31:1049–1064. http://dx.doi.org/10.1080/0266476042000280409.

      [5] Henze, N. (1986). A probabilistic representation of the skew–normal distribution. Scandinavian Journal of Statistics 13:271–275.

      [6] Hoyt, J.P. (1968) a simple approximation to the standard normal probability density function. American Statistician.22, No.2, 25-56. http://dx.doi.org/10.2307/2681984.

      [7] Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika 36:149–176. http://dx.doi.org/10.1093/biomet/36.1-2.149.

      [8] Johnson, N. L., Kotz, S., Balakrishnan, N. (1995). Continuous Univeriate Distributions –Volume 2. New York: Wiley.

      [9] Leiva, V., Barros, M., Paula, G. A., Galea, M. (2007). Influence diagnostics in log - Birnbaum–Saunders regression models with censored data. Computational Statistics and Data Analysis 51:5694–5707. http://dx.doi.org/10.1016/j.csda.2006.09.020.

      [10] Leiva, V., Vilca, F., Balakrishnan, N., Saunhueza, A. (2010). A skewed sinh–normal distribution and its properties and application to air pollution. Communication in Statistics – Theory and Methods 39:426–443. http://dx.doi.org/10.1080/03610920903140171.

      [11] Owen, D. B. (1956). Tables for computing bivariate normal probabilities. Annals of Mathematical Statistics. 27, 1075–1090. http://dx.doi.org/10.1214/aoms/1177728074.

      [12] Rieck, J. R. (1989). Statistical Analysis for the Birnbaum–Saunders Fatigue Life Distribution. Unpublished Ph.D. thesis, Department of Mathematical Sciences, Clemson University, USA.

      [13] Rieck,J.R., Nedelman, J. R. (1991). A log-linear model for the Birnbaum–Saunders distribution. Technometrics 33:51–60. http://dx.doi.org/10.2307/1269007.

      [14] Saunhueza, A., Leiva, V., Balakrishnan, N. (2008). The generalized Birnbaum–Saunders distribution and its theory, methodology and application. Communication in Statistics – Theory and Methods 37:645–670. http://dx.doi.org/10.1080/03610920701541174.


 

View

Download

Article ID: 4610
 
DOI: 10.14419/ijasp.v3i1.4610




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.