Confidence intervals and prediction intervals for two-parameter negative binomial distributions

Abstract

Problems of finding confidence intervals (CIs) and prediction intervals (PIs) for two-parameter negative binomial distributions are considered. Simple CIs for the mean of a two-parameter negative binomial distribution based on some large sample methods are proposed and compared with the likelihood CIs. Proposed CIs are not only simple to compute, but also better than the likelihood CIs for moderate sample sizes. Prediction intervals for the mean of a future sample from a two-parameter negative binomial distribution are also proposed and evaluated for their accuracy. The methods are illustrated using two examples with real life data sets.

Keywords: Joint sampling approach; maximum likelihood estimates; over-dispersion; poisson distribution; prediction intervals; score method.