  Modeling sparse data such as microbiome and transcriptomics (RNA-seq) data is
very challenging due to the exceeded number of zeros and skewness of the
distribution. Many probabilistic models have been used for modeling sparse
data, including Poisson, negative binomial, zero-inflated Poisson, and
zero-inflated negative binomial models. One way to identify the most
appropriate probabilistic models for zero-inflated or hurdle models is based on
the p-value of the Kolmogorov-Smirnov (KS) test. The main challenge for
identifying the probabilistic model is that the model parameters are typically
unknown in practice. This paper derives the maximum likelihood estimator (MLE)
for a general class of zero-inflated and hurdle models. We also derive the
corresponding Fisher information matrices for exploring the estimator's
asymptotic properties. We include new probabilistic models such as
zero-inflated beta binomial and zero-inflated beta negative binomial models.
Our application to microbiome data shows that our new models are more
appropriate for modeling microbiome data than commonly used models in the
literature.
