The distributions of spectral characteristics and their correlations with fluence, peak flux, or duration, are essential in understanding the nature of GRBs. However, the selection effects involved in detecting GRBs can distort these distributions. Here, we discuss how to deal with selection effects involving the peak energyEpof the GRB&ngr;F&ngr;spectrum, which suffers from both an upper and lower threshold. We describe a new method to account for this double-sided truncation, and show that the true distribution ofEpis significantly different from the observed distribution. ©1998 American Institute of Physics.