Felix Famoye

Zero-Inflated Generalized Poisson Regression Model with an Application to Domestic Violence Data

The generalized Poisson regression model has been used to model dispersed count data. It is a good competitor to the negative binomial re- gression model when the count data is over-dispersed. Zero-inflated Poisson and zero-inflated negative binomial regression models have been proposed for the situations where the data generating process results into too many zeros. In this paper, we propose a zero-inflated generalized Poisson (ZIGP) regression model to model domestic violence data with too many zeros. Es- timation of the model parameters using the method of maximum likelihood is provided. A score test is presented to test whether the number of zeros is too large for the generalized Poisson model to adequately fit the domestic violence data.

Restricted generalized poisson regression model

The family of generalized Poisson distribution has been found useful in describing over-dispersed and under-dispersed count data. We propose the use of restricted generalized Poisson regression model to predict a response variable affected by one or more explanatory variables. Approximate tests for the adequacy of the model and the estimation of the parameters are considered. Restricted generalized Poisson regression model has been applied to an observed data set.

On the Generalized Poisson Regression Model with an Application to Accident Data

In this paper a random sample of drivers aged sixty-five years or older was selected from the Alabama Department of Public Safety Records. The data in the sample has information on many variables including the number of accidents, demographic information, driving habits, and medication. The purpose of the sample was to assess the effects of demographic factors, driving habits, and medication use on elderly drivers. The generalized Poisson regression (GPR) model is considered for identifying the relationship between the number of accidents and some covariates. About 59% of drivers who rate their quality of driving as average or below are involved in automobile accidents. Drivers who take calcium channel blockers show a significantly reduced risk of about 34.5%. Based on the test for the dispersion parameter and the goodness-of-fit measure for the accident data, the GPR model performs as good as or better than the other regression models.

Weibull-pareto distribution and its applications

In this article, a new distribution, namely, Weibull-Pareto distribution is defined and studied. Various properties of the Weibull-Pareto distribution are obtained. The distribution is found to be unimodal and the shape of the distribution can be skewed to the right or skewed to the left. Results for moments, limiting behavior, and Shannons entropy are provided. The method of modified maximum likelihood estimation is proposed for estimating the model parameters. Several real data sets are used to illustrate the applications of Weibull-Pareto distribution.

The gamma-normal distribution: Properties and applications

In this paper, some properties of gamma-X family are discussed and a member of the family, the gamma-normal distribution, is studied in detail. The limiting behaviors, moments, mean deviations, dispersion, and Shannon entropy for the gamma-normal distribution are provided. Bounds for the non-central moments are obtained. The method of maximum likelihood estimation is proposed for estimating the parameters of the gamma-normal distribution. Two real data sets are used to illustrate the applications of the gamma-normal distribution.

On generating T-X family of distributions using quantile functions

The cumulative distribution function (CDF) of the T-X family is given by R{W(F(x))}, where R is the CDF of a random variable T, F is the CDF of X and W is an increasing function defined on [0, 1] having the support of T as its range. This family provides a new method of generating univariate distributions. Different choices of the R, F and W functions naturally lead to different families of distributions. This paper proposes the use of quantile functions to define the W function. Some general properties of this T-X system of distributions are studied. It is shown that several existing methods of generating univariate continuous distributions can be derived using this T-X system. Three new distributions of the T-X family are derived, namely, the normal-Weibull based on the quantile of Cauchy distribution, normal-Weibull based on the quantile of logistic distribution, and Weibull-uniform based on the quantile of log-logistic distribution. Two real data sets are applied to illustrate the flexibility of the distributions.

A rich family of generalized Poisson regression models with applications

The Poisson regression (PR) model is inappropriate for modeling over- or under-dispersed (or inflated) data. Several generalizations of PR model have been proposed for modeling such data. In this paper, a rich family of generalized Poisson regression (GPR) models is reviewed in detail. The family has a wide range of applications in various disciplines including agriculture, econometrics, patent applications, species abundance, medicine, and use of recreational facilities. For illustrating the usefulness of the family, several applications with different situations are given. For example, hospital discharge counts are modeled using GPR and other generalized models, in which the applied models show that household size, education, and income are positively related to diagnosis-related groups (DRGs) hospital discharges. One of the advantages of using the family is that it lets data determine which model is appropriate for a given situation. It is expected that the results discussed in the paper would enhance our understanding of various forms of count data originating from primary health care facilities and medical domains.

Bivariate generalized Poisson distribution with some applications

The univariate generalized Poisson probability model has many applications in various areas such as engineering, manufacturing, survival analysis, genetic, shunting accidents, queuing, and branching processes. A correlated bivariate version of the univariate generalized Poisson distribution is defined and studied. Estimation of its parameters and some of its properties are also discussed.

Modelling count response variables in informetric studies: Comparison among count, linear, and lognormal regression models

The purpose of the study is to compare the performance of count regression models to those of linear and lognormal regression models in modelling count response variables in informetric studies. Identified count response variables in informetric studies include the number of authors, the number of references, the number of views, the number of downloads, and the number of citations received by an article. Also of a count nature are the number of links from and to a website. Data were collected from the United States Patent and Trademark Office (www.uspto.gov), an open access journal (www.informationr.net/ir/), Web of Science, and Macleans magazine. The datasets were then used to compare the performance of linear and lognormal regression models with those of Poisson, negative binomial, and generalized Poisson regression models. It was found that due to over-dispersion in most response variables, the negative binomial regression model often seems to be more appropriate for informetric datasets than the Poisson and generalized Poisson regression models. Also, the regression analyses showed that linear regression model predicted some negative values for five of the nine response variables modelled, and for all the response variables, it performed worse than both the negative binomial and lognormal regression models when either Akaikes Information Criterion (AIC) or Bayesian Information Criterion (BIC) was used as the measure of goodness of fit statistics. The negative binomial regression model performed significantly better than the lognormal regression model for four of the response variables while the lognormal regression model performed significantly better than the negative binomial regression model for two of the response variables but there was no significant difference in the performance of the two models for the remaining three response variables.

T-normal family of distributions: a new approach to generalize the normal distribution

The idea of generating skewed distributions from normal has been of great interest among researchers for decades. This paper proposes four families of generalized normal distributions using the T-X framework. These four families of distributions are named as T-normal families arising from the quantile functions of (i) standard exponential, (ii) standard log-logistic, (iii) standard logistic and (iv) standard extreme value distributions. Some general properties including moments, mean deviations and Shannon entropy of the T-normal family are studied. Four new generalized normal distributions are developed using the T-normal method. Some properties of these four generalized normal distributions are studied in detail. The shapes of the proposed T-normal distributions can be symmetric, skewed to the right, skewed to the left, or bimodal. Two data sets, one skewed unimodal and the other bimodal, are fitted by using the generalized T-normal distributions.AMS 2010 Subject Classification60E05; 62E15; 62P10