# The Mixture Poisson Exponential – Inverse Gaussian Regression Model : An application in Health Services

@inproceedings{Dniz2016TheMP, title={The Mixture Poisson Exponential – Inverse Gaussian Regression Model : An application in Health Services}, author={Emilio G{\'o}mez – D{\'e}niz and Enrique Calderı́n – Ojeda}, year={2016} }

In this paper a mixed Poisson regression model for count data is introduced. This model is derived by mixing the Poisson distribution with the one–parameter continuous exponential–inverse Gaussian distribution. The obtained probability mass function is over–dispersed and unimodal with modal value located at zero. Estimation is performed by maximum likelihood. As an application, the demand for health services among people 65 and over is examined using this regression model since empirical…

No Paper Link Available

## 3 Citations

### EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking

- Mathematics
- 2020

This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an…

### The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking

- MathematicsEuropean Actuarial Journal
- 2018

This paper presents the Negative Binomial-Inverse Gaussian regression model for approximating the number of claims as an alternative to mixed Poisson regression models that have been widely used in…

### The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking

- MathematicsEuropean Actuarial Journal
- 2018

This paper presents the Negative Binomial-Inverse Gaussian regression model for approximating the number of claims as an alternative to mixed Poisson regression models that have been widely used in…

## References

SHOWING 1-10 OF 20 REFERENCES

### Demand for Medical Care by the Elderly: A Finite Mixture Approach

- Economics, Mathematics
- 1997

In this article we develop a finite mixture negative binomial count model that accommodates unobserved heterogeneity in an intuitive and analytically tractable manner. This model, the standard…

### A mixed poisson–inverse‐gaussian regression model

- Mathematics
- 1989

The mixed Poisson–inverse-Gaussian distribution has been used by Holla, Sankaran, Sichel, and others in univariate problems involving counts. We propose a Poisson–inverse-Gaussian regression model…

### Models for count data with endogenous participation

- Economics
- 2009

We present several extensions of the Poisson and negative binomial models for count data based on the lognormal model for latent heterogeneity in the conditional means. The lognormal model provides a…

### EM Algorithm for Mixed Poisson and Other Discrete Distributions

- MathematicsASTIN Bulletin
- 2005

Mixed Poisson distributions are widely used in various disciplines including actuarial applications. The family of mixed Poisson distributions contains several members according to the choice of the…

### Econometric models based on count data. Comparisons and applications of some estimators and tests

- Mathematics, Economics
- 1986

This paper deals with specification, estimation and tests of single equation reduced form type equations in which the dependent variable takes only non-negative integer values. Beginning with Poisson…

### Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method

- Mathematics
- 1974

SUMMARY To define a likelihood we have to specify the form of distribution of the observations, but to define a quasi-likelihood function we need only specify a relation between the mean and variance…

### Negative Binomial Regression

- Economics, Psychology
- 2007

Preface 1. Introduction 2. The concept of risk 3. Overview of count response models 4. Methods of estimation and assessment 5. Assessment of count models 6. Poisson regression 7. Overdispersion 8.…

### Mixed Poisson Distributions

- Mathematics
- 2005

Mixed Poisson distributions have been used in a wide range of scientific fields for modeling nonhomogeneous populations. This paper aims at reviewing the existing literature on Poisson mixtures by…

### Generalized Linear Models for Insurance Data

- Computer Science
- 2008

This practical, rigorous book treats GLMs, covers all standard exponential family distributions, extends the methodology to correlated data structures, and discusses recent developments which go beyond the GLM.