Brazilian Journal of Probability and Statistics

The extended generalized half-normal distribution

Jeniffer J. Duarte Sanchez, Wanessa W. da Luz Freitas, and Gauss M. Cordeiro

Full-text: Open access

Abstract

Fatigue is a structural damage which occurs when a material is exposed to stress and tension fluctuations. We propose and study the extended generalized half-normal distribution for modeling skewed fatigue life data. The new model contains as special cases the half-normal and generalized half-normal (Comm. Statist. Theory Methods 37 (2008) 1323–1337) distributions. Various of its structural properties are derived, including the density function, moments, quantile and generating functions, mean deviations and order statistics. We investigate maximum likelihood estimation of the model parameters. An application illustrates the potentiality of the new distribution.

Article information

Source
Braz. J. Probab. Stat., Volume 30, Number 3 (2016), 366-384.

Dates
Received: March 2014
Accepted: February 2015
First available in Project Euclid: 29 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1469807217

Digital Object Identifier
doi:10.1214/15-BJPS284

Mathematical Reviews number (MathSciNet)
MR3531689

Zentralblatt MATH identifier
1381.62033

Keywords
Exponentiated generalized class generalized half-normal distribution Kwmaraswamy model maximum likelihood estimation survival function

Citation

Duarte Sanchez, Jeniffer J.; da Luz Freitas, Wanessa W.; Cordeiro, Gauss M. The extended generalized half-normal distribution. Braz. J. Probab. Stat. 30 (2016), no. 3, 366--384. doi:10.1214/15-BJPS284. https://projecteuclid.org/euclid.bjps/1469807217


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References

  • Aarts, R. M. (2000). Lauricella functions. Available at www.mathworld.com/LauricellaFunctions.html. From MathWorld—A Wolfram Web Resouce, created by Eric W. Weisstein.
  • Chen, G. and Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology 27, 154–161.
  • Cooray, K. and Ananda, M. M. A. (2008). A generalization of the half-normal distribution with applications to lifetime data. Communications in Statistics. Theory and Methods 37, 1323–1337.
  • Cordeiro, G. M., Ortega, E. M. M. and da Cunha, D. C. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science 11, 1–27.
  • Gradshteyn, I. S. and Ryzhik, I. M. (2000). Table of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press.
  • Kenney, J. F. and Keeping, E. S. (1962). Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand.
  • Moors, J. J. A. (1998). A quantile alternative for kurtosis. Journal of the Royal Statistical Society. Series D. The Statistician 37, 25–32.
  • Nadarajah, S. and Kotz, S. (2006). The exponentiated-type distributions. Acta Applicandae Mathematicae 92, 97–111.
  • Sharafi, M. and Behboodian, J. (2008). The Balakrishnan skew-normal density. Statistical Papers 49, 769–778.
  • Pescim, R. R., Demétrio, C. G. B., Cordeiro, G. M., Ortega, E. M. M. and Urbano, M. R. (2010). The beta generalized half-normal distribution. Computational Statistics and Data Analysis 54, 945–957.
  • Steinbrecher, G. (2002). Taylor expansion for inverse error function around origin. Working paper, Univ. Craiova.
  • Trott, M. (2006). The Mathematica Guidebook for Symbolics. New York: Springer.