Conditional Goodness-of-Fit Tests for Discrete Distributions

In this paper, we address the problem of testing goodness-of-fit for discrete distributions, where focus on geometric distribution. We define new likelihood-based tests using beta-geometric distribution and type I Weibull as alternative distributions. The are compared in a simulation study, also classical considered comparison. Throughout paper consider conditional given minimal sufficient statistic under null hypothesis, which enables calculation exact p values. For purpose, method is developed drawing samples from negative binomial explain briefly how approach can be modified binomial, Poisson It finally noted that may extended to other distributions having same statistic, by Metropolis–Hastings algorithm.