On the Superiority of the Negative Binomial Test Over the Binomial Test for Estimating the Bit Error Rate

This paper examines the binomial and negative binomial tests for estimating the bit error rate using Monte Carlo simulations. Whereas the estimator error variances and simulation times do not recommend one test over the other, confidence interval analysis and test design criteria recommend the negative binomial test for estimating a small bit error rate based on a limited number of error events. The Clopper-Pearson interval length is much more consistent for the negative binomial test in the small bit error rate case. The logarithmically centered confidence interval is introduced and analyzed. For a given confidence interval length and confidence probability, the negative binomial test requires fewer error events than the binomial test. The asymptotic analyses of the Clopper-Pearson and logarithmically-centered confidence intervals yield useful design criteria for the negative binomial test in a way that is not possible for the binomial test.