On the Folded Normal Distribution

Tsagris, Michail and Beneki, Christina and Hassani, Hossein (2013): On the Folded Normal Distribution. Published in: Mathematics , Vol. 2, No. 1 (14 February 2014): pp. 12-28.

Abstract

The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also assessed using different criteria. The maximum likelihood estimates and confidence intervals for the parameters are obtained using the asymptotic theory and bootstrap method. The coverage of the confidence intervals is also examined.

• Item Type: MPRA Paper
• Language: English
• Keywords: folded normal distribution, entropy, Kullback–Leibler, maximum likelihood estimates

References

1. Leone, F.C.; Nelson, L.S.; Nottingham, R.B. The folded normal distribution. Technometrics 1961,3, 543–550.

2. Lin, H.C. The measurement of a process capability for folded normal process data. Int. J. Adv. Manuf. Technol. 2004, 24, 223–228.

3. Chakraborty, A.K.; Chatterjee, M. On multivariate folded normal distribution. Sankhya 2013, 75, 1–15.

4. Elandt, R.C. The folded normal distribution: Two methods of estimating parameters from moments. Technometrics 1961, 3, 551–562.

5. Johnson, N.L. The folded normal distribution: Accuracy of estimation by maximum likelihood. Technometrics 1962, 4, 249–256.

6. Johnson, N.L. Cumulative sum control charts for the folded normal distribution. Technometrics 1963, 5, 451–458.

7. Sundberg, R. On estimation and testing for the folded normal distribution. Commun. Stat.-Theory Methods 1974, 3, 55–72.

8. Kim, H.J. On the ratio of two folded normal distributions. Commun. Stat.-Theory Methods 2006, 35, 965–977.

9. Liao, M.Y. Economic tolerance design for folded normal data. Int. J. Prod. Res. 2010, 48, 4123–4137.

10. Nelder, J.A.; Mead, R. A simplex method for function minimization. Comput. J. 1965, 7, 308–313.

11. Johnson, N.L; Kotz, S.; Balakrishnan, N. Continuous Univariate Distributions; John Wiley & Sons, Inc.: New York, NY, USA, 1994.

12. Psarakis, S.; Panaretos, J. The folded t distribution. Commun. Stat.-Theory Methods 1990, 19, 2717–2734.

13. Psarakis, S.; Panaretos, J. On some bivariate extensions of the folded normal and the folded t distributions. J. Appl. Stat. Sci. 2000, 10, 119–136.

14. Kullback, S. Information Theory and Statistics; Dover Publications: New York, NY, USA, 1977.

15. R Development Core Team. R: A Language and Environment for Statistical Computing, 2012. Available online: http://www.R-project.org/ (accessed on 1 December 2013).

16. Yee, T.W. The VGAM package for categorical data analysis. J. Stat. Softw. 2010, 32, 1–34.

17. Efron, B.; Tibshirani, R. An Introduction to the Bootstrap; Chapman and Hall/CRC: New York, NY, USA, 1993.

18. MacMahon, S.; Norton, R.; Jackson, R.; Mackie, M.J.; Cheng, A.; Vander Hoorn, S.; Milne, A.; McCulloch, A. Fletcher challenge-university of Auckland heart and health study: Design and baseline findings. N. Zeal. Med. J. 1995, 108, 499–502.