TITLE:
Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data
AUTHORS:
Mohamed M. Shoukri, Maha M. Aleid
KEYWORDS:
Queuing Models, Overdispersion, Moment Estimators, Delta Method, Bootstrap, Maximum Likelihood Estimation, Fisher’s Information, Orthogonal Polynomials, Regression Models, RNE-Seq Data
JOURNAL NAME:
Open Journal of Statistics,
Vol.12 No.2,
April
19,
2022
ABSTRACT: Background: The Poisson and the Negative Binomial distributions are commonly used to
model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial
has a variance larger than the mean and therefore both models are appropriate
to model over-dispersed count data. Objectives: A new
two-parameter probability distribution called the Quasi-Negative Binomial
Distribution (QNBD) is being studied in this paper,
generalizing the well-known negative binomial distribution. This model
turns out to be quite flexible for analyzing count data. Our main objectives
are to estimate the parameters of the proposed distribution and to discuss its applicability to genetics data. As an
application, we demonstrate that the QNBD regression representation is utilized to model genomics data sets. Results: The new distribution is shown to provide a good fit with respect to the
“Akaike Information Criterion”, AIC, considered a measure of model goodness of
fit. The proposed distribution may serve as a viable alternative to other
distributions available in the literature for modeling count data exhibiting
overdispersion, arising in various fields of scientific investigation such as
genomics and biomedicine.