A Simulation-Free Exact Conditional Goodness-of-Fit Test for The Binomial Distribution

ABSTRACT: Several exact testing methods for continuous distributions, asymptotic as well as simulation based exact methods for both- discrete and continuous cases have been developed for analyzing goodness-of-fit, a priori. An exact Kolmogorov-Smirnov type goodness-of-fit test is developed for checking whether the data comes from a binomial distribution or not. This is a conditional test; p-value is calculated as the conditional probability given the sample total and hence the success probability need not be specified under the null hypothesis. Instead of using simulation, p-value is calculated using a sequential procedure and hence the inference procedure is simulationfree. Properties of the test, some examples, power comparisons with other existing techniques are also provided.