Recent applications, particularly in genomics and imaging, call for testing large number of hypothesis tests at the same time. The False Discovery Rate (FDR) has been proposed and recognized as a powerful criterion in these contexts. Approximations of FDR such as local false discovery rate (lfdr) has been proposed and justified using two-group models, for example Efron (2007a). A generalization of two-group models is proposed. Under this framework, we study various approximations of false discovery rate and their validity. The connection with skew normality is also addressed.

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