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Biometrika 1984 71(3):633-636; doi:10.1093/biomet/71.3.633
© 1984 by Biometrika Trust
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MISCELLANEA

Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions

J. S. HUANG and SAMUEL KOTZ

Department of Mathematics and Statistics, University of Guelph Guelph, Ontario, Canada
Department of Management and Statistics, University of Maryland College Park, Maryland, U.S.A.

In this note we determine the natural parameter space of the iterated Farlie-Gumbel-Morgenstern distribution, and thereby show that the maximum correlation is higher than was previously known. We also show that just one single iteration can result in tripling the covariance for certain marginals. Finally, we show that there exist no marginals for which the single iteration will bring about higher negative correlation.

Key Words: Expected value of order statistics • Farlie-Gumbel-Morgenstern distribution • Maximum correlation • Minimum correlation • Parameter space


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