International Journal of Statistical Distributions and Applications
Volume 3, Issue 4, December 2017, Pages: 61-66
Received: Aug. 28, 2017;
Accepted: Sep. 13, 2017;
Published: Nov. 1, 2017
Views 407 Downloads 26
Ampalavanar Nanthakumar, Department of Mathematics, State University of New York at Oswego, Oswego NY, USA
The paper presents a Copula based approach to test for a two component bivariate mixture distribution. The regular joint density is modeled by using the Copula and then the Locally Most Powerful test (LMP) test is derived by using this Copula based regular density. This is a fairly simple test compared to the dip / depth test developed by Hartigan. Our simulation results show that this Copula based (LMP) test is very powerful in detecting a mixture.
A Copula Based Test for a Two Component Bivariate Mixture Distribution, International Journal of Statistical Distributions and Applications.
Vol. 3, No. 4,
2017, pp. 61-66.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Engelman, L., and Hartigan, J. A. Percentage of a test for clusters. Journal of American Statistical Association (1969), 64, 1647-1648.
Frees, E. W., and Valdez, E. A. Understanding Relationships Using Copulas. North American Actuarial Journal (1998), 2(1), 1-25.
Giocomelli, F., Wiener, J., Kruskal, J. B., Pomeran, J. W., and Loud, A. V. Sub-Populations of blood lymphocytes as demonstrated by quantitative cytochemistry. Journal of Histochemistry and Cytochemistry (1971), 19, 426-433.
Hartigan, J. A., and Hartigan, P. M. The Dip Test of Unimodality. Annals of Statistics (1985), 13, 1, 70-84.
Nanthakumar, A. On the mixture Gaussian Copula to study the suitability of diagnostic tests. Sri Lankan Journal of Applied Statistics (2013), 14(2), 121-132.
Nanthakumar, A., Ganesalingam, S., and Ganesh, S. On Copula based discriminant rule. Journal of Statistics & Management Systems (2013), 16(6), 401-417.
Nanthakumar, A. Multivariate Kurtosis as a tool for comparing Copula Models”, International Journal of Statistics and Probability (2016), 5(4), 67-78.
Nelson, R. B. An Introduction to Copulas (2006), Springer.
Rao, C. R. Linear Statistical Inference and its Applications (1973), 2nd Edition, Wiley, New York.
Sklar, A. Fonctions de repartition a n dimensions et leurs marges. Publications de L’ Institut de Statistique de L’ Universite de Paris (1959), 8, 229-231.