References
- Azzalini A. A class of distributions which includes the normal ones. Scand J Statist. 1985;12:171–178.
- Azzalini A. Further results on a class of distributions which includes the normal ones. Statistica. 1986;46:199–208.
- Azzalini A. The skew-normal distribution and related multivariate families. With discussion by Marc G. Genton and a rejoinder by the author. Scand J Statist. 2005;32:159–200. doi: 10.1111/j.1467-9469.2005.00426.x
- Gupta RC, Brown N. Reliability studies of the skew-normal distribution and its application to a strength–stress model. Comm Statist Theory Methods. 2001;30:2427–2445. doi: 10.1081/STA-100107696
- Gupta AK, Chen T. Goodness-of-fit tests for the skew-normal distribution. Commun Statist Theory Methods. 2001;30:907–930.
- Gupta AK, Chen JT. A class of multivariate skew-normal models. Ann Inst Statist Math. 2004;56:305–315. doi: 10.1007/BF02530547
- Gupta AK, Chang FC, Huang WJ. Some skew-symmetric models. Random Oper Stoch Equ. 2002;10:133–140. doi: 10.1515/rose.2002.10.2.133
- Lin TI, Lee JC, Yen SY. Finite mixture modelling using the skew normal distribution. Statist Sin. 2007;17:909–927.
- Tsai TR. Skew normal distribution and the design of control charts for averages. Int J Reliab Qual Saf Eng. 2007;14:49–63. doi: 10.1142/S0218539307002507
- Tsai TR, Chiang JY. The design of acceptance control chart for non-normal data. J Chinese Inst Ind Eng. 2008;25:127–135.
- Li CI, Su NC, Su PF, Shyr Y. The design of X¯ and R control charts for skew normal distributed data. Comm Statist Theory Methods. 2014. ahead-of-print.
- Razzaghi M. A Hierarchical model for the skew-normal distribution with application in developmental neurotoxicology. Commun Statist Theory Methods. 2014;43:1859–1872. doi: 10.1080/03610926.2012.675115
- Su NC, Chiang JY, Chen SC, Tsai TR, Shyr Y. Economic design of two-stage control charts with skewed and dependent measurements. Int J Adv Manuf Tech. 2014;73:1387–1397. doi: 10.1007/s00170-014-5897-1
- Gupta AK, Chen JT. On the sample characterization criterion for normal distributions. J Statist Comput Simul. 2003;73:155–163. doi: 10.1080/00949650215867
- Chen JT, Gupta AK, Nguyen TT. The density of the skew normal sample mean and its applications. J Statist Comput Simul. 2004;74:487–494. doi: 10.1080/0094965031000147687
- Gupta AK, González-Farías G, Domínguez-Molina JA. A multivariate skew normal distribution. J Multi Anal. 2004;89:181–190. doi: 10.1016/S0047-259X(03)00131-3
- Genz A, Bretz F. Computation of multivariate normal and t probabilities. New York: Springer; 2009.
- Lukacs E. Characterization of populations by properties of suitable statistics. Proc. 3rd Berkeley symp. math. statist. and prob., Vol. 2. Los Angels: University of California Press; 1956.
- Seber GAF. A matrix handbook for statisticians. Hoboken (NJ): John Wiley & Sons; 2008.
- Azzalini A, Dalla-Valle AD. The multivariate skew-normal distribution. Biometrika. 1996;83:715–726. doi: 10.1093/biomet/83.4.715
- Azzalini A, Capitanio A. Statistical applications of the multivariate skew normal distribution. J R Soc Ser B. 1999;61:579–602. doi: 10.1111/1467-9868.00194
- Gupta AK, Huang WJ. Quadratic forms in skew normal variates. J Math Anal Appl. 2002;273:558–564. doi: 10.1016/S0022-247X(02)00270-6
- Azzalini A, Capitanio A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J R Soc Ser B. 2003;65:367–389. doi: 10.1111/1467-9868.00391
- Jamalizadeh A, Khosravi M, Balakrishnan N. Recurrence relations for distributions of a skew-t and a linear combination of order statistics from a bivariate-t. Comput Statist Data Anal. 2009;53:847–852. doi: 10.1016/j.csda.2008.11.002
- Huang WJ, Su NC, Teng HY. On some study of skew-t distributions. Commun Statist Theory Methods. 2014. Available from: http://dx.doi.org/10.1080/03610926.2012.700369.
- Schoonhoven M, Does RJ. The X¯ control chart under non-normality. Qual Reliab Eng Int. 2010;26:167–176.
- Joanes DN, Gill CA. Comparing measures of sample skewness and kurtosis. Statistician. 1998;47:183–189.