On Poisson-exponential-Tweedie models for ultra-overdispersed data

08/23/2019
by   Rahma Abid, et al.
0

We introduce a new class of Poisson-exponential-Tweedie (PET) mixture in the framework of generalized linear models for ultra-overdispersed count data. The mean-variance relationship is of the form m+m^2+ϕ m^p, where ϕ and p are the dispersion and Tweedie power parameters, respectively. The proposed model is equivalent to the exponential-Poisson-Tweedie models arising from geometric sums of Poisson-Tweedie random variables. In this respect, the PET models encompass the geometric versions of Hermite, Neyman Type A, Pólya-Aeppli, negative binomial and Poisson inverse Gaussian models. The algorithms we shall propose allow us to estimate the real power parameter, which works as an automatic distribution selection. Instead of the classical Poisson, zero-shifted geometric is presented as the reference count distribution. Practical properties are incorporated into the PET of new relative indexes of dispersion and zero-inflation phenomena. Simulation studies demonstrate that the proposed model highlights unbiased and consistent estimators for large samples. Illustrative practical applications are analyzed on count datasets; in particular, PET models for data without covariates and PET regression models. The PET models are compared to Poisson-Tweedie models showing that parameters of both models are adopted to data.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/29/2018

Reparametrization of COM-Poisson Regression Models with Applications in the Analysis of Experimental Data

In the analysis of count data often the equidispersion assumption is not...
research
04/30/2021

Models Based on Exponential Interarrival Times for Single-Unusual-Event Count Data

At least one unusual event appears in some count datasets. It will lead ...
research
04/22/2020

ARMA Models for Zero Inflated Count Time Series

Zero inflation is a common nuisance while monitoring disease progression...
research
03/27/2020

Transition Models for Count Data: a Flexible Alternative to Fixed Distribution Models

A flexible semiparametric class of models is introduced that offers an a...
research
07/08/2020

Modelling excess zeros in count data: A new perspective on modelling approaches

We consider models underlying regression analysis of count data in which...
research
05/30/2023

Control Charts for Poisson Counts based on the Stein-Chen Identity

If monitoring Poisson count data for a possible mean shift (while the Po...
research
10/04/2019

Bregman-divergence-guided Legendre exponential dispersion model with finite cumulants (K-LED)

Exponential dispersion model is a useful framework in machine learning a...

Please sign up or login with your details

Forgot password? Click here to reset