Prediction intervals based on partial observations for some discrete distributions

Prediction limits of the following type are considered for the binomial, hypergeometric, and negative-binomial distributions. For the binomial distribution, suppose X_r successes have occurred in the first r trials, and based on this partial information it is desired to predict the total number of successes X _s (r<s), which will have occurred by trial s. Similar results are considered for the Poisson and negative-binomial distributions. The results are expressed in terms of well known distributions which have been tabulated, but it is quite tedious to carry out the procedures based on available tables. Normal (Gaussian) approximations are provided which make these methods convenient to apply