  We develop the distribution of the number of hypotheses found to be
statistically significant using the rule from Benjamini and Hochberg (1995) for
controlling the false discovery rate (FDR). This distribution has both a small
sample form and an asymptotic expression for testing many independent
hypotheses simultaneously. We propose a parametric distribution
$\,\Psi_I(\cdot)\,$ to approximate the marginal distribution of p-values under
a non-uniform alternative hypothesis. This distribution is useful when there
are many different alternative hypotheses and these are not individually well
understood. We fit $\,\Psi_I\,$ to data from three cancer studies and use it to
illustrate the distribution of the number of notable hypotheses observed in
these examples. We model dependence of sampled p-values using a copula model
and a latent variable approach. These methods can be combined to illustrate a
power analysis in planning a large study on the basis of a smaller pilot study.
We show the number of statistically significant p-values behaves approximately
as a mixture of a normal and the Borel-Tanner distribution.
