Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data

作     者：Mohamed M. Shoukri Maha M. Aleid Mohamed M. Shoukri;Maha M. Aleid

作者机构：Department of Epidemiology and Biostatistics Schulich School of Medicine and Dentistry University of Western Ontario London Canada Department of Biostatistics Epidemiology and Scientific Computing King Faisal Specialist Hospital and Research Center Riyadh Saudi Arabia 

出 版 物：《Open Journal of Statistics》 (统计学期刊（英文）)

年 卷 期：2022年第12卷第2期

页      面：216-237页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Queuing Models Overdispersion Moment Estimators Delta Method Bootstrap Maximum Likelihood Estimation Fisher’s Information Orthogonal Polynomials Regression Models RNE-Seq Data 

摘      要：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.