DOI QR코드

DOI QR Code

Some counterexamples of a skew-normal distribution

  • Zhao, Jun (Department of Applied Statistics, Konkuk University) ;
  • Lee, Sang Kyu (Department of Applied Statistics, Konkuk University) ;
  • Kim, Hyoung-Moon (Department of Applied Statistics, Konkuk University)
  • 투고 : 2019.07.17
  • 심사 : 2019.09.19
  • 발행 : 2019.11.30

초록

Counterexamples of a skew-normal distribution are developed to improve our understanding of this distribution. Two examples on bivariate non-skew-normal distribution owning marginal skew-normal distributions are first provided. Sum of dependent skew-normal and normal variables does not follow a skew-normal distribution. Continuous bivariate density with discontinuous marginal density also exists in skew-normal distribution. An example presents that the range of possible correlations for bivariate skew-normal distribution is constrained in a relatively small set. For unified skew-normal variables, an example about converging in law are discussed. Convergence in distribution is involved in two separate examples for skew-normal variables. The point estimation problem, which is not a counterexample, is provided because of its importance in understanding the skew-normal distribution. These materials are useful for undergraduate and/or graduate teaching courses.

키워드

참고문헌

  1. Azzalini A and Capitanio A (2014). The Skew-Normal and Related Families, Cambridge University Press, New York.
  2. Fang KT, Kotz S, and Ng KW (1990). Symmetric Multivariate and Related Distributions, Chapman and Hall, New York.
  3. Kim HM and Genton MG (2011). Characteristic functions of scale mixtures of multivariate skew-normal distributions, Journal of Multivariate Analysis, 102, 1105-1117. https://doi.org/10.1016/j.jmva.2011.03.004
  4. Lin GD and Stoyanov J (2009). The logarithmic skew-normal distributions are moment-indeterminate, Journal of Applied Probability, 46, 909-916. https://doi.org/10.1239/jap/1253279858
  5. Romano JP and Siegel AF (1986). Counterexamples in Probability and Statistics, Wadsworth & Brooks/Cole Advanced Books & Software, California.
  6. Stoyanov JM (2013). Counterexamples in Probability (3rd ed), Dover Publications, New York.