A simple improved inferential method for some discrete distributions

In this article, some simple methods for testing and estimating the parameters of some discrete distributions are proposed. For hypothesis testing, a new test is obtained by combining the usual exact test and an alternative exact test. The exact properties of the usual exact test, the alternative exact test and the combined test are evaluated numerically for the binomial and Poisson distributions. Numerical studies show that the combined test is more powerful than the usual one while controlling the sizes satisfactorily. Furthermore, the combined procedure produces confidence intervals that are practically equivalent to the intervals based on some other complex methods. The methods are also illustrated for the hypergeometric and negative binomial distributions.