Truncated-exponential skew-symmetric distributions

References

• Ferreira JTAS, Steel MFJ. A constructive representation of univariate skewed distributions. J Amer Statist Assoc. 2006;101:823–829. doi: 10.1198/016214505000001212
   Web of Science ®Google Scholar
• Jones MC. Families of distributions arising from distributions of order statistics (with discussion). Test. 2004;13:1–43. doi: 10.1007/BF02602999
   Web of Science ®Google Scholar
• Fernández C, Steel MFJ. On Bayesian modeling of fat tails and skewness. J Amer Statist Assoc. 1998;93:359–371.
   Web of Science ®Google Scholar
• Azzalini A. A class of distributions include the normal ones. Scand J Stat. 1985;12:171–178.
   Web of Science ®Google Scholar
• Azzalini A. Further results on a class of distributions which includes the normal ones. Statistica. 1986;XLVI:199–208.
   Google Scholar
• Azzalini A, Dalla Valle A. The multivariate skew-normal distribution. Biometrika. 1996;83:715–726. doi: 10.1093/biomet/83.4.715
   Web of Science ®Google Scholar
• Azzalini A, Capitanio A. Statistical applications of the multivariate skew normal distribution. J R Stat Soc B. 1999;61:579–602. doi: 10.1111/1467-9868.00194
   Google Scholar
• Arnold BC, Beaver RJ. The skew-Cauchy distribution. Statist Probab Lett. 2000;49:285–290. doi: 10.1016/S0167-7152(00)00059-6
   Web of Science ®Google Scholar
• Pewsey A. Problems of inference for Azzalini's skew-normal distribution. J Appl Statist. 2000;27:351–360. doi: 10.1080/02664760050120542
   Web of Science ®Google Scholar
• Loperfido N. Quadratic forms of skew-normal random vectors. Statist Probab Lett. 2001;54:381–387. doi: 10.1016/S0167-7152(01)00103-1
   Web of Science ®Google Scholar
• Arnold BC, Beaver RJ. Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion). Test. 2002;11:7–54. doi: 10.1007/BF02595728
   Web of Science ®Google Scholar
• Nadarajah S, Kotz S. Skewed distributions generated by the normal kernel. Statist Probab Lett. 2003;65:269–277. doi: 10.1016/j.spl.2003.07.013
   Web of Science ®Google Scholar
• Gupta RC, Gupta RD. Generalized skew normal model. Test. 2004;13:501–524. doi: 10.1007/BF02595784
   Web of Science ®Google Scholar
• Behboodian J, Jamalizadeh A, Balakrishnan N. A new class of skew-Cauchy distributions. Statist Probab Lett. 2006;76:1488–1493. doi: 10.1016/j.spl.2006.03.008
   Web of Science ®Google Scholar
• Nadarajah S, Kotz S. Skew distributions generated from different families. Acta Appl Math. 2006;91:1–37. doi: 10.1007/s10440-006-9017-6
   Web of Science ®Google Scholar
• Huang WJ, Chen HY. Generalized skew Cauchy distribution. Statist Probab Lett. 2007;77:1137–1147. doi: 10.1016/j.spl.2007.02.006
   Web of Science ®Google Scholar
• Sharafi M, Behboodian J. The Balakrishnan skew-normal density. Statist Papers. 2007;49:769–778. doi: 10.1007/s00362-006-0038-z
   Web of Science ®Google Scholar
• van Zwet WR. Convex transformations of random variables. Mathematical Centre Tracts 7. Amsterdam: Mathematisch Centrum; 1964.
   Google Scholar
• Shannon CE. Prediction and entropy of printed English. Bell System Tech J. 1951;30:50–64. doi: 10.1002/j.1538-7305.1951.tb01366.x
   Google Scholar
• Rényi A. On measures of entropy and information. Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, Vol. I, Berkeley: University of California Press; 1961. p. 547–561.
   Google Scholar
• Hoskings JRM. L-moments: analysis and estimation of distribution using linear combinations of order statistics. J R Stat Soc B. 1990;52:105–124.
   Google Scholar
• Lehmann EL, Casella G. Theory of point estimation. 2nd ed. New York: Springer-Verlag; 1998.
   Google Scholar
• Rudin W. Principles of mathematical analysis. 3rd ed. New York: McGraw-Hill Book Company; 1976.
   Google Scholar
• Nadarajah S. Explicit expressions for moments of normal order statistics. Demonstratio Math. 2007;40:575–579.
   Google Scholar
• Exton H. Handbook of hypergeometric integrals: theory, applications, tables, computer programs. New York: Halsted Press; 1978.
   Google Scholar
• Nadarajah S. Explicit expressions for moments of t order statistics. C R Math. 2007;345:523–526. doi: 10.1016/j.crma.2007.10.027
   Web of Science ®Google Scholar
• Johnson NL, Kotz S, Balakrishnan N. Continuous univariate distributions. 2nd ed. Vol. 2, New York: John Wiley & Sons; 1995.
   Google Scholar
• Arnold BC, Groeneveld RA. Measuring skewness with respect to the mode. Amer Statist. 1995;49:34–38.
   Web of Science ®Google Scholar
• R Development Core Team, 2011. A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.
   Google Scholar
• Nadarajah S. Extremes of daily rainfall in west central Florida. Climatic Change. 2005;69:325–342. doi: 10.1007/s10584-005-1812-y
   Web of Science ®Google Scholar
• Blom G. Statistical estimates and transformed beta-variables. New York: John Wiley & Sons; 1958.
   Google Scholar
• Chambers J, Cleveland W, Kleiner B, Tukey P. Graphical methods for data analysis. London: Chapman & Hall; 1983.
   Google Scholar
• Azzalini A, Capitanio A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J R Stat Soc B. 2003;65:367–389. doi: 10.1111/1467-9868.00391
   Google Scholar
• Jones MC, Faddy MJ. A skew extension of the t distribution, with applications. J R Stat Soc B. 2003;65:159–174. doi: 10.1111/1467-9868.00378
   Google Scholar
• Ma Y, Genton MG. Flexible class of skew-symmetric distributions. Scand J Statist. 2004;31:459–468. doi: 10.1111/j.1467-9469.2004.03_007.x
   Web of Science ®Google Scholar
• Azzalini A, Genton MG. Robust likelihood methods based on the skew-t and related distributions. Int Statist Rev. 2008;76:106–129. doi: 10.1111/j.1751-5823.2007.00016.x
   Web of Science ®Google Scholar