Modeling sparse and discrete omics data such as microbiome and transcriptomics is challenging due to exceeded number of zeros. Many probabilistic models have been used, including Poisson, negative binomial, zero-inflated Poisson, and zero-inflated negative binomial models. In this paper, we propose a statistical procedure for identifying the most appropriate discrete probabilistic models for zero-inflated or Hurdle models based on the p-value of the discrete Kolmogorov-Smirnov (KS) test. We develop a general procedure for estimating the parameters for a large class of zero-inflated models and Hurdle models. We also develop a general likelihood ratio test based on Neyman-Pearson lemma for choosing the best model when appropriate ones are more than one.