A. Conde-Sánchez

A hyper-Poisson regression model for overdispersed and underdispersed count data

The Poisson regression model is the most common framework for modeling count data, but it is constrained by its equidispersion assumption. The hyper-Poisson regression model described in this paper generalizes it and allows for over- and under-dispersion, although, unlike other models with the same property, it introduces the regressors in the equation of the mean. Additionally, regressors may also be introduced in the equation of the dispersion parameter, in such a way that it is possible to fit data that present overdispersion and underdispersion in different levels of the observations. Two applications illustrate that the model can provide more accurate fits than those provided by alternative usual models.

A generalized Waring regression model for count data

A regression model for count data based on the generalized Waring distribution is developed. This model allows the observed variability to be split into three components: randomness, internal differences between individuals and the presence of other external factors that have not been included as covariates in the model. An application in the field of sports illustrates its capacity for modelling data sets with great accuracy. Moreover, this yields more information than a model based on the negative binomial distribution.

A triparametric discrete distribution with complex parameters

Rodríguez-Aviet al. (2002) give a general description of a discrete distribution generated by the Gaussian hypergeometric function with complex parameters and provide a detailed study of a biparametric distribution, namedCBPD, under conditions where the complex parameters have no real part. In this paper we present a more complete study of the discrete distribution obtained in the general case. Thus, its main probabilistic properties are described, convergence results are generalized and, finally, methods of estimation are developed with some examples of applications.

Estimation of Parameters in Gaussian Hypergeometric Distributions

Abstract Some methods for estimating parameters in distributions generated by the Gaussian hypergeometric function are developed in this article: specifically, methods based on relations between moments and/or frequencies, estimators obtained by the minimum chi-square procedure and the method of maximum likelihood are considered. The asymptotic relative efficiencies of estimators with explicit formulae are compared. Finally, two real examples are given in order to illustrate these methods.

A new generalization of the Waring distribution

A tetraparametric univariate distribution generated by the Gaussian hypergeometric function that includes the Waring and the generalized Waring distributions as particular cases is presented. This distribution is expressed as a generalized beta type I mixture of a negative binomial distribution, in such a way that the variance of the tetraparametric model can be split into three components: randomness, proneness and liability. These results are extensions of known analogous properties of the generalized Waring distribution. Two applications in the fields of sport and economy are included in order to illustrate the utility of the new distribution compared with the generalized Waring distribution.

Gaussian Hypergeometric Probability Distributions for Fitting Discrete Data

The distributions generated by the Gaussian hypergeometric function compose a tetraparametric family that includes many of the most common discrete distributions in the literature. In this article, probability aspects related to the whole family are reviewed and methods of estimation for fitting them to real data are developed. Several applied examples are also provided to illustrate the procedures and compare the methods of estimation.

Estimation and Inference in Complex Triparametric Pearson Distributions

Abstract The complex triparametric Pearson distribution is an extension of the Gaussian hypergeometric probability distribution with complex parameters that provides adequate random models for data originating from different fields. In the present article, relations between moments and probabilities are employed to obtain minimum χ2 estimators of the parameters. We compare the asymptotic relative efficiency of these estimators with those obtained by several methods. We also develop a test of hypotheses in selecting a two-parameter family from a three-parameter family of distributions. Finally, some examples are provided to illustrate these methods.

Modelling using an extended Yule distribution

A biparametric discrete distribution that extends the Yule distribution is presented. It belongs to the family of distributions generated by the Gaussian hypergeometric function and it can be expressed as a generalized beta mixture of a geometric distribution. The introduction of a new parameter makes the model very suitable to fit the empiric distribution tails and the effect of infinite variance is not possible. Several examples show more accurate fits when the extended distribution is used and the results are compared with other biparametric extensions of the Yule distribution.

Computational techniques in the study of discrete distributions generated by the function 3 F 2

In this paper, we present the use of computational aspects in the study of the family of discrete distributions generated by the hypergeometric function 3 F 2, which is a univariate extension of the Gaussian hypergeometric function. These computational techniques allow us to obtain the probability mass function, the mean, the mode in an explicit form as well as the knowledge of the most important properties. We can also obtain a summation result and implement different methods of estimation. Finally, we present an example of an application to real data already fitted by other discrete distributions.