Faustino Prieto

Modeling the probabilistic distribution of the impact factor

The study of the informetric distributions, such as distributions of citations and impact factors is one of the most relevant topics in the current informetric research. Several laws for modeling impact factor based on ranks have been proposed, including Zipf, Lavalette and the two-exponent law proposed by Mansilla et al. (2007). In this paper, the underlying probabilistic quantile function corresponding to the Mansillas two-exponent law is obtained. This result is particularly relevant, since it allows us to know the underlying population, to learn about all its features and to use statistical inference procedures. Several probabilistic descriptive measures are obtained, including moments, Lorenz and Leimkuhler curves and Gini index. The distribution of the order statistics is derived. Least squares estimates are obtained. The different results are illustrated using the data of the impact factors in eight relevant scientific fields.

Modelling road accident blackspots data with the discrete generalized Pareto distribution

This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed.

A general method for generating parametric Lorenz and Leimkuhler curves

Let L0 consider an initial Lorenz curve. In this paper we propose a general methodology for obtaining new classes of parametric Lorenz or Leimkuhler curves that contain the original curve as limiting or special case. The new classes introduce additional parameters in the original family, providing more flexibility for the new families. The new classes are built from an ordered sequence of power Lorenz curves, assuming that the powers are distributed according to some convenient discrete random variable. Using this method we obtain many of the families proposed in the literature, including the classical proposal of Bradford (1934), Kakwani and Podder (1973) and others. We obtain some inequality measures and population functions for the proposed families.

On the Estimation of the Global Income Distribution Using a Parsimonious Approach

Abstract This paper aims to estimate the global income distribution during the nineties using limited information. In a first stage, we obtain national income distributions considering a model with two parameters. In particular, we propose to use the so-called Lame distributions, which are curved versions of the Sigh-Maddala and Dagum distributions. The main feature of this family is that they represent parsimonious models which can fit income data adequately with just two parameters and whose Lorenz curves are characterized by only one parameter. In a second stage, global and regional distributions are derived from a finite mixture of these families using population shares. We test the validity of the model, comparing it with other two-parameter families. Our estimates of different inequality measures suggest that global inequality presents a decreasing pattern mainly driven by the fall of the differences across countries during the course of the study period that offsets the increase in disparities within countries.

Bivariate beta-generated distributions with applications to well-being data

The class of beta-generated distributions (Commun. Stat. Theory Methods 31:497–512, 2002; TEST 13:1–43, 2004) has received a lot of attention in the last years. In this paper, three new classes of bivariate beta-generated distributions are proposed. These classes are constructed using three different definitions of bivariate distributions with classical beta marginals and different covariance structures. We work with the bivariate beta distributions proposed in (J. Educ. Stat. 7:271–294, 1982; Metrika 54:215–231, 2001; Stat. Probability Lett. 62:407–412, 2003) for the first proposal, in (Stat. Methods Appl. 18: 465–481, 2009) for the second proposal and (J. Multivariate Anal. 102:1194–1202, 2011) for the third one. In each of these three classes, the main properties are studied. Some specific bivariate beta-generated distributions are studied. Finally, some empirical applications with well-being data are presented.Mathematics Subject Classification (2000)62E15; 60E05

A generalization of the power law distribution with nonlinear exponent

Abstract The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.

The n-fold convolution of a finite mixture of densities

Abstract In this paper, the probability density function of the n-fold convolution of a finite mixture of densities is obtained. The new density is again a finite mixture of densities. In this way, the formula recently given by Ma [N.-Y. Ma, A comment on “On the distribution of Ma and King, Applied Mathematics and Computation” 218 (2011) 202–203] for a two-fold convolution is interpreted and extended and a correct expression for the formula provided by Nadarajah [S. Nadarajah, On the distribution of Ma and King, Applied Mathematics and Computation 189 (2007) 732–733] is given. Several relevant examples are provided, including the convolution for the generalized exponential-sum distribution.