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JSRI 2018, 14(2): 219-246 Back to browse issues page
A Perturbed Half-normal Distribution and Its Applications
Eisa Mahmoudi *1, Reihaneh Lalehzari, Rahmat Sadat Meshkat
1- , mahmoudi@yazd.ac.ir
Abstract:   (3280 Views)
In this paper, a new generalization of the half-normal distribution which is called the perturbed half-normal distribution is introduced. The new distribution belongs to a family of distributions which includes the half-normal distribution along with an extra parameter to regulate skewness. The probability density function (pdf) is derived and some various properties of the new distribution are obtained. The derived properties include the cumulative distribution function (cdf), the $r$th moment, moment generating function, characteristic function, mean deviation about the mean and estimation of the parameters using the method of moments and maximum likelihood. Finally, the flexibility and potentiality of the new distribution is illustratedin an application to two real data sets.
Keywords: Error function, half-normal distribution, hypergeometric function, skewness, moment generating function.
Full-Text [PDF 1709 kb]   (945 Downloads)    
Type of Study: Research | Subject: General
Received: 2016/12/23 | Accepted: 2018/01/21 | Published: 2018/03/17
1. Aarset, M.V. (1987). How to Identify Bathtub Hazard Rate. IEEE Transactions Reliability, 36, 106-108. [DOI:10.1109/TR.1987.5222310]
2. Aigner, D.J., Lovell, C.A.K. and Schmidt, P. (1977). Formulation and Estimation of Stochastic Frontier Production Models. J. Econometrics, 6, 21-37. [DOI:10.1016/0304-4076(77)90052-5]
3. Azzalini, A. (1985). A Class of Distributions which Includes the Normal Ones. Scand. J. Statist., 12, 171-178.
4. Bland, J.M. and Altman, D.G. (1999). Measuring Agreement in Method Comparison Studies. Stat. Meth. Med. Res, 8, 135-160. [DOI:10.1177/096228029900800204]
5. Chen, G. and Balakrishnan, N. (1995). A General Purpose Approximate Goodness-of-fit Test. Journal of Quality Technology, 27, 154-161. [DOI:10.1080/00224065.1995.11979578]
6. Chou, C.Y. and Liu, H.R. (1998). Properties of the Half-normal Distribution and Its Application to Quality Control. Journal of Industrial Technology, 14, 4-7.
7. Cooray, K. and Ananda, M.M.A. (2008). A Generalization of the Half-normal Distribution with Applications to Lifetime Data. Commun. Statist. Theor. Meth., 37, 1323-1337. [DOI:10.1080/03610920701826088]
8. Daniel, C. (1959). Use of Half-normal Plots in Interpreting Factorial Two-level Experiments. Technometrics, 1, 311-341. [DOI:10.1080/00401706.1959.10489866]
9. Dobzhansky, T. and Wright, S. (1947). Genetics of Natural Populations X. Dispersal Rates in Drosophila Pseudoobscura. Genetics, 28, 304-340.
10. Flecher C., Allard, D. and Naveau, P. (2009). Truncated Skew-normal Distributions: Estimation by Weighted Moments and Application to Climatic Data. INRA Research Report 39, Available from: http://www.avignon.inra.fr/content/download/7204/111974/version/1/ file/RR2009-39.pdf.
11. Gelman, A. (2006). Prior Distributions for Variance Parameters in Hierarchical Models. Bayesian analysis, 1, 515-534. [DOI:10.1214/06-BA117A]
12. Glaser, R.E. (1980). Bathtub and Related Failure Rate Characterizations. Journal of the American Statistical Association, 75, 667-672. Gradshteyn, I.S. and Ryzhik, I.M. (2000). Table of Integrals, Series, and Products. Academic Press, San Diego. [DOI:10.1080/01621459.1980.10477530]
13. Haberle, J.G. (1991). Strength and Failure Mechanisms of Unidirectional Carbon Fibre-Reinforced Plastics Under Axial Compression. Unpublished Ph.D. thesis, Imperial College, London.
14. Hinkley, D. (1977). On Quick Choice of Power Transformations. The American Statistician, 26, 67-69. [DOI:10.2307/2346869]
15. Leslie, H. Miller (1956). Table of Percentage Points of Kolmogorov Statistics. J. Am. Stat. Assoc., 51, 111-121. [DOI:10.1080/01621459.1956.10501314]
16. Meeusen, W.J. and van den Broeck, J. (1977). Efficiency Estimation from Cobb Douglas Production Functions with Composed Error. Int. Econ. Rev, 8, 435-444. [DOI:10.2307/2525757]
17. Mitchell, M.R. and Landgraf, R.W. (1996). Advances in Fatigue Lifetime Predictive Techniques: 3rd Volume, ASTM International. [DOI:10.1520/STP1292-EB]
18. Nichols, M.D. and Padgett, W.J. (2006). A Bootstrap Control Chart for Weibull Percentiles. Quality and Reliability Engineering International, 22, 141-151. [DOI:10.1002/qre.691]
19. Pescim, R.R., Demetrio, C.G.B., Cordeiro, G.M., Ortega, E.M.M. and Urbano, M.R. (2009). The Beta Generalized Half-normal Distribution. Comput. Stat. Data Anal., 54, 945-957. [DOI:10.1016/j.csda.2009.10.007]
20. Pewsey, A. (2002). Large-sample Inference for the General Half-normal Distribution. Commun. Statist. Theor. Meth., 31, 1045-1054. [DOI:10.1081/STA-120004901]
21. Pewsey, A. (2004). Improved Likelihood based Inference for the General Half-normal Distribution. Commun. Statist. Theor. Meth., 33, 197-204. [DOI:10.1081/STA-120028370]
22. Radson, D. and Alwan, L.C. (1995). Detecting Variance Reductions using the Moving Range. Quality Engineering, 8, 165-178. [DOI:10.1080/08982119508904612]
23. Smith, R.L. (1985). Maximum Likelihood Estimation in a Class of Nonregular Cases. Biometrika, 72, 67-90. [DOI:10.1093/biomet/72.1.67]
24. Wiper, M.P., Giron, F.J. and Pewsey, A. (2008). Objective Bayesian Inference for the Half-normal and Half-t distributions. Commun. Statist. Theor. Meth., 37, 3165-3185. [DOI:10.1080/03610920802105184]
25. Watson, G.S. (1961). Goodness-of-fit Tests on a Circle. Biometrika, 48, 109-114. [DOI:10.1093/biomet/48.1-2.109]
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Mahmoudi E, Lalehzari R, Meshkat R S. A Perturbed Half-normal Distribution and Its Applications. JSRI. 2018; 14 (2) :219-246
URL: http://jsri.srtc.ac.ir/article-1-272-en.html

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Volume 14, Issue 2 (3-2018) Back to browse issues page
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