  This paper introduces a new discrete distribution suggested by curtailed
sampling rules common in early-stage clinical trials. We derive the
distribution of the smallest number of independent Bernoulli(p) trials needed
in order to observe either s successes or t failures. The closed form
expression for the distribution as well as the compound distribution are
derived. Properties of the distribution are shown and discussed. A case study
is presented showing how the distribution can be used to monitor sequential
enrollment of clinical trials with binary outcomes as well as providing
post-hoc analysis of completed trials.
