%0 Journal Article
%T Empirical Bayesian Approach to Testing Homogeneity of Several Means of Inflated Poisson Distributions (IPD)
%A Mohamed M. Shoukri
%A Maha Aleid
%J Open Journal of Statistics
%P 285-299
%@ 2161-7198
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojs.2023.133015
%X <strong>Objectives:</strong><span><span><span style=\"font-family:&quot;\"><span style=\"font-family:Verdana;\"> We introduce a special form of the Generalized Poisson Distribution. The
distribution has one parameter, yet it has a variance that is larger than the
mean a phenomenon known as ˇ°over dispersionˇ±. We discuss potential applications
of the distribution as a model of counts, and under the assumption of
independence we will perform statistical inference on the ratio of two means,
with generalization to testing the homogeneity of several means. </span><b><span style=\"font-family:Verdana;\">Methods:</span></b><span><span style=\"font-family:Verdana;\"> Bayesian methods depend on the choice of the prior distributions of
the population parameters. In this paper, we describe a Bayesian approach </span><span style=\"font-family:Verdana;\">for estimation and inference on the parameters of
several independent Inflated</span><span style=\"font-family:Verdana;\"> Poisson (IPD) distributions with two
possible priors, the first is the reciprocal </span><span style=\"font-family:Verdana;\">of
the square root of the Poisson parameter and the other is a conjugate Gamma
prior</span><span style=\"font-family:Verdana;\">. The parameters of Gamma distribution are estimated in the
empirical Bayesian framework using the maximum likelihood (ML) solution using
nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest
posterior confidence intervals on the ratio of two IPD parameters and test the
homogeneity of several populations. </span></span><b><span style=\"font-family:Verdana;\">Results</span></b></span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><b><span style=\"font-family:Verdana;\">: </span></b></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">We encountered convergence problem in estimating the
hyperparameters of the posterior distribution using the NLMIXED. However,
direct maximization of the predictive density produced solutions to the maximum
likelihood equations. We apply the methodologies to RNA-SEQ read count data of
gene expression values.</span></span></span>
%K Distributions of Over-Dispersed Counts
%K Lagrange Class of Distributions
%K Knowledge Transfer
%K Gamma Prior
%K Posterior Inference
%K Wilson-Hilferty Transformation
%K RNA_SEQ Read Counts Data
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=125625