The beta skew t distribution and its properties

References

• Ahn, S., J. H. Kim, and V. Ramaswami. 2012. A new class of models for heavy tailed distributions in finance and insurance risk. Insurance: Mathematics and Economics 51(1):43–52.
   Web of Science ®Google Scholar
• Arellano-Valle, R. B., and M. G. Genton. 2005. On fundamental skew distributions. Journal of Multivariate Analysis 96(1):93–116. doi:10.1016/j.jmva.2004.10.002.
   Web of Science ®Google Scholar
• Azzalini, A. 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12(2):171–178.
   Web of Science ®Google Scholar
• Azzalini, A., and A. Capitanio. 2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65(2):367–89. doi:10.1111/rssb.2003.65.issue-2.
   Web of Science ®Google Scholar
• Azzalini, A., and A. Capitanio. 2014. The Skew-Normal and Related Families, Vol. 3. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Azzalini, A., and A. Dalla Valle. 1996. The multivariate skew-normal distribution. Biometrika 83(4):715–26. doi:10.1093/biomet/83.4.715.
   Web of Science ®Google Scholar
• Cooray, K., and M. M. Ananda. 2005. Modeling actuarial data with a composite lognormal-pareto model. Scandinavian Actuarial Journal (5):321–34. doi:10.1080/03461230510009763.
   Google Scholar
• Cordeiro, G. M., and M. De Castro. 2011. A new family of generalized distributions. Journal of Statistical Computation and Simulation 81(7):883–98. doi:10.1080/00949650903530745.
   Web of Science ®Google Scholar
• Cordeiro, G. M., S. Nadarajah, et al. 2011. Closed-form expressions for moments of a class of beta generalized distributions. Brazilian Journal of Probability and Statistics. 25(1):14–33. doi:10.1214/09-BJPS109.
   Web of Science ®Google Scholar
• Eling, M. 2012. Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?. Insurance: Mathematics and Economics 51(2):239–48.
   Web of Science ®Google Scholar
• Eugene, N., C. Lee, and F. Famoye. 2002. Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods 31(4):497–512. doi:10.1081/STA-120003130.
   Web of Science ®Google Scholar
• Farias, R. B., M. H. Montoril, and J. A. Andrade. 2016. Bayesian inference for extreme quantiles of heavy tailed distributions. Statistics & Probability Letters 113:103–07. doi:10.1016/j.spl.2016.02.020.
   Web of Science ®Google Scholar
• Frees, E. W., and E. A. Valdez. 1998. Understanding relationships using copulas. North American Actuarial Journal 2(1):1–25. doi:10.1080/10920277.1998.10595667.
   Google Scholar
• Gupta, A. K. 2003. Multivariate skew t-distribution. Statistics: A Journal of Theoretical and Applied Statistics 37(4):359–63. doi:10.1080/715019247.
   Web of Science ®Google Scholar
• Gupta, A. K., and S. Nadarajah. 2004. Handbook of Beta Distribution and its Applications. Boca Raton, FL: CRC press.
   Google Scholar
• Hasan, A. M. (2013). A Study of Non-Central Skew t Distributions and Their Applications in Data Analysis and Change Point Detection. PhD thesis, Bowling Green State University.
   Google Scholar
• Hosking, J. R. 1990. L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society. Series B (Methodological) 52(1):105–124.
   Google Scholar
• Huang, W.-J., and Y.-H. Chen. 2006. Quadratic forms of multivariate skew normalsymmetric distributions. Statistics & Probability Letters 76(9):871–79. doi:10.1016/j.spl.2005.10.018.
   Web of Science ®Google Scholar
• Jones, M. 2004. Families of distributions arising from distributions of order statistics. Test 13(1):1–43. doi:10.1007/BF02602999.
   Web of Science ®Google Scholar
• Mameli, V., and M. Musio. 2013. A generalization of the skew-normal distribution: The beta skew-normal. Communications in Statistics-Theory and Methods 42(12):2229–44. doi:10.1080/03610926.2011.607530.
   Web of Science ®Google Scholar
• McNeil, A. J. 1997. Estimating the tails of loss severity distributions using extreme value theory. ASTIN Bulletin 27(01):117–37. doi:10.2143/AST.27.1.563210.
   Google Scholar
• Rêgo, G., and S. Nadarajah. 2011. On some properties of beta normal distribution. Communications in Statistics Theory and Methods 41(20):3722–38. doi:10.1080/03610926.2011.568156.
   Web of Science ®Google Scholar
• Resnick, S. I. 1997. Discussion of the danish data on large fire insurance losses. ASTIN Bulletin 27(01):139–51. doi:10.2143/AST.27.1.563211.
   Google Scholar
• Rohatgi, V. K., and A. M. Ehsanes Saleh. 1988. A class of distributions connected to order statistics with nonintegral sample size. Communications in Statistics-Theory and Methods 17(6):2005–12. doi:10.1080/03610928808829728.
   Web of Science ®Google Scholar
• Shafiei, S., and M. Doostparast. 2014. Balakrishnan skew-t distribution and associated statistical characteristics. Communications in Statistics-Theory and Methods 43(19):4109–22. doi:10.1080/03610926.2012.701697.
   Web of Science ®Google Scholar
• Silva, G. O., E. M. Ortega, and G. M. Cordeiro. 2010. The beta modified Weibull distribution. Lifetime Data Analysis 16(3):409–30. doi:10.1007/s10985-010-9161-1.
   PubMed Web of Science ®Google Scholar
• Thukral, A. K. 2014. Factorials of real negative and imaginary numbers-a new perspective. SpringerPlus 3(1):658. doi:10.1186/2193-1801-3-658.
   PubMedGoogle Scholar