Moment tests of fit for some discrete distributions with ecological applications

We present moment orientated tests of fit for some discrete distributions used in ecological applications. The distributions covered are the Poisson, negative binomial, zero-truncated Poisson, logarithmic, zero-inflated Poisson, binomial, beta-binomial, geometric, Neyman Type A and the bivariate Poisson. Each distribution is illustrated by reference to ecological data. The tests of fit we give are often more powerful than traditional chi-squared tests.