Test of independence for generalized Farlie–Gumbel–Morgenstern distributions

✍ Scribed by Bilgehan Güven; Samual Kotz

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 167 KB
• Volume: 212
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2006.11.029

✦ Synopsis

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.