Estimation of Parameters of the Unified Skew Normal Distribution Using the Method of Weighted Moments
Tóm tắt
Modeling skewness based on the class of skew normal distributions has drawn considerable attention in recent years. However, there still remain lots of challenges related to the inferences about the parameters of the skew normal distribution. In this article, we study the weighted moments estimators for the unified skew normal distribution. Our analytical results and numerical illustrations show that weighted moments method accurately estimates the parameters of the unified skew normal distribution.
Tài liệu tham khảo
Arellano-Valle, R. B., and A. Azzalini. 2006. On the unification of families of skew-normal distributions. Scand. J. Stat., 33, 561–574.
Azzalini, A., and A. Capitanio. 1999. Statistical applications of the multivariate skew normal distributions. J. R. Stat. Soc. Ser. B, 61, 579–602.
Dalla Valle, A. 2004. The skew-normal distribution. In Skew-elliptical distributions and their applications: A journey beyond normality, ed. M. G. Genton, 3–24. Boca Raton, FL, Chapman and Hall/CRC.
Domingnez-Molina, J. A., G. Gonzalez-Farias, and A. K. Gupta. 2001. General multivariate skew normal distribution. Department of Mathematics and Statistics, Bowling Green State University. Tech. rep. no. 01-09.
Flecher, C., P. Naveau, and D. Allard. 2009. Estimating the closed skew-normal distribution parameters using weighted moments. Stat. Probability Lett., 79(19), 1977–1984.
Genton, M. G., ed. 2004. Skew-elliptical distributions and their applications: A journey beyond normality. Boca Raton, FL, Chapman and Hall/CRC.
Gupta, A. K., and M. A. Aziz. 2011. Quadratic forms in unified skew normal random vectors. Department of Mathematics and Statistics, Bowling Green State University. Tech. rep. no. 11–11.
Gupta, A. K., and M. A. Aziz. 2011. Robust comonotonic lower convex order bound approximations for the distribution of terminal wealth. Department of Mathematics and Statistics, Bowling Green State University. Tech. rep. no. 11–13.
Gupta, A. K., and T. Chen. 2001. Goodness-of-fit tests for the skew-normal distribution. Commun. Stat. Simulation Comput., 30, 907–930.
Gupta, A. K., M. A. Aziz, and W. Ning. 2011. Additive properties of unified skew normal random vectors. Department of Mathematics and Statistics, Bowling Green State University. Tech. rep. no. 11–06.
Liseo, B. 1990. The skew-normal class of densities: inferential aspects from a Bayesian viewpoint (in Italian). Statistics, 50, 59–70.
Nguyen, T. T., J. A. T. Sanqui, D. M. Nguyen, and A. K. Gupta. 2009. A note on the maximum likelihood estimator of the skew parameter in a skew-normal distribution. Far East J. Theor. Stat. 28(1), 1–8.
Pewsey, A. 2000. Problems of inference for Azzalini’s skewnormal distribution. J. Appl. Stat., 27(7), 859–870.
Sanqui, J. A. T., T. T. Nguyen, and A. K. Gupta. 2008. Estimation in Roberts’ correlation model for twin studies. Int. Math. Forum, 3(14), 661–670.