Test of independence for generalized Farlie-Gumbel-Morgenstern distributions

  • Authors:

  • Bilgehan Güven;Samual Kotz

  • Affiliations:

  • Statistics Department, Middle East Technical University, 06531 Ankara, Turkey;Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC 20052, USA

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2008

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Abstract

Given a pair of absolutely continuous random variables (X,Y) distributed as the generalized Farlie-Gumbel-Morgenstern (GFGM) distribution, we develop a test for testing the hypothesis: X and Y are independent vs. the alternative; X and Y are positively (negatively) quadrant dependent above a preassigned degree of dependence. The proposed test maximizes the minimum power over the alternative hypothesis. Also it possesses a monotone increasing power with respect to the dependence parameter of the GFGM distribution. An asymptotic distribution of the test statistic and an approximate test power are also studied.