José Rodríguez-Avi

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.

Estimating the count of completeness errors in geographic data sets by means of a generalized Waring regression model

In this article, we propose a statistical model for estimating the probable number of completeness errors (omissions plus commissions) in a cell (a map tile or cluster) of a data set to guide updating or improvement efforts. The number of completeness errors is a count data variable related to some exogenous covariates that may also be known for each cell (e.g. count of features, rural or urban typology, etc.) and to other unknown variation sources. We propose and adjust a generalized Waring regression model for counting these errors in cells of 1 × 1 km2 on the Topographic Map of Andalusia (Spain). This model is compared with the Poisson regression model and the negative binomial regression model and performs better. The empirical relationship established by the model indicates that the number of completeness errors is related to the following exogenous covariates: the number of cartographic features of the data set, the fact that the cell covers a littoral or urban zone and the spatial division of the contracted suppliers. For cells having less than 5 errors, most of the variability corresponds to unknown external factors (liability), but when the number of errors rises, the greater part of the variability is due to unknown internal characteristics of each cell (proneness). With these estimations, the producer can derivate statistical summaries and spatial representations and develop better planning of production activities such as actualization.

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.

A Method of Positional Quality Control Testing for 2D and 3D Line Strings

This article presents a positional quality acceptance control method for 2D and 3D line strings based on a statistical hypothesis test. Two statistical models are applied together: a Binomial Model is applied over a Base Model. By means of the Base Model the method can be applied to any parametric or non-parametric error model. The Base Model represents the hypothesis about the error behavior. The Binomial Model is fixed and consists of counting the number F of fail events in a sample of a determined size. The π parameter of the Binomial Model is derived from the Base Model by means of a desired tolerance. By comparing the probabilities associated to F and π a statistical acceptance/rejection decision is achieved. This method allows us to know and control the users and producers risk of acceptance/rejection. An example using a 2D line string data set from a commercial product is presented. The extension of the method to the 3D line string case is also presented. In order to facilitate the application of the method, some tables linking π with F and the control sample sizes are presented.

Using International Standards to Control the Positional Quality of Spatial Data

Abstract A positional quality control method based on the application of the International Standard ISO 2859 is proposed. This entails a common framework for dealing with the control of all other spatial data quality components (e.g., completeness, consistency, etc.). We propose a relationship between the parameters “acceptable quality level” and “limiting quality” of the international standard and positional quality by means of observed error models. This proposal does not require any assumption for positional errors (e.g., normality), which means that the application is universal. It can be applied to any type of positional and geometric controls (points, line-strings), to any dimension (1D, 2D, 3D, etc.) and with parametric or non-parametric error models (e.g., lidar). This paper introduces ISO 2859, presents the statistical bases of the proposal and develops two examples of application, the first dealing with a lot-by-lot control and the second, isolated lot control.

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.