Multivariate distributions defined in terms of contours

The paper deals with the problem of using contours as the basis for defining probability distributions. First, the most general probability densities with given contours are obtained and the particular cases of circular and elliptical contours are dealt with. It is shown that the so-called elliptically contoured distributions do not include all possible cases. Next, the case of contours defined by polar coordinates is analyzed including its simulation and parameter estimation. Finally, the case of cumulative distribution functions with given contours is discussed. Several examples are used for illustrative purposes.     

A hierarchy of lorenz curves based on the generalized tukey's lambda distribution

A hierarchy of Lorenz curves based on the generalized Tukey's Lambda distribution is proposed. Representations of the corresponding distribution and density function are also provided, together with popular inequality measures. Estimation methods are suggested. Finally, a comparison with other parametric families of Lorenz curves is established.     

Bivariate income distributions with lognormal conditionals

In this paper, the most general bivariate distribution with lognormal conditionals is fully characterized, using the methodology proposed by [3]. The properties of the new family are studied in detail, including marginal and conditional distributions, regression functions, dependence measures, moments and inequality measures. The new distribution is very broad, and contains as a particular case the classical bivariate lognormal distribution. Several subfamilies are studied and a generalization of the basic model is discussed. Finally, we present an empirical application. We estimate and compare the basic model proposed in the paper with a classical model, using data from the European Community Household Panel in different periods of time.     

A hierarchy of lorenz curves based on the generalized tukey's lambda distribution

A hierarchy of Lorenz curves based on the generalized Tukey's Lambda distribution is proposed. Representations of the corresponding distribution and density function are also provided, together with popular inequality measures. Estimation methods are suggested. Finally, a comparison with other parametric families of Lorenz curves is established.     

Bivariate distributions with second kind beta conditionals

In this paper the most general bivariate distributions with second kind beta conditionals is fully characterized. This family is closed under inversions and the conditional moments are shown to be rational functions of the conditioned variable. Two subfamilies of dependent distributions is shown to have second kind beta marginals too. Finally, as a particular case, the most general bivariate distribution with second kind Pareto conditionals is characterized.     

Bayesian estimation of incomplete data using conditionally specified priors

In this article, a class of conjugate prior for estimating incomplete count data based on a broad class of conjugate prior distributions is presented. The new class of prior distributions arises from a conditional perspective, making use of the conditional specification methodology and can be considered as the generalization of the form of prior distributions that have been used previously in the estimation of incomplete count data well. Finally, some examples of simulated and real data are given.     

Distorted Lorenz curves: models and comparisons

The economic literature contains many parametric models for the Lorenz curve. A number of these models can be obtained by distorting an original Lorenz curve $L$ by a function $h$ , giving rise to a distorted Lorenz curve ${\widetilde{L}}=h\circ L$ . In this paper, we study, in a unified framework, this family of curves. First, we explore the role of these curves in the context of the axiomatic structure of Aaberge (2001) for orderings on the set of Lorenz curves. Then, we describe some particular models and investigate how changes in the parameters in the baseline Lorenz curve $L$ affect the transformed curve ${\widetilde{L}}$ . Our results are stated in terms of preservation of some stochastic orders between two Lorenz curves when both are distorted by a common function.     

Robust Bayesian bonus-malus premiums under the conditional specification model

The conditional specification technique introduced by Arnold et al. (Conditional specification of statistical models. Springer series in statistics. Springer, New York, 1999) was used in Sarabia et al. (Astin Bull 34(1):85–98, 2004) to obtain bonus-malus premiums. The Poisson distribution for which the parameter is a function of the classical structure parameter was used and a new class of prior distributions appeared in a natural way. This model contains, as a particular case, the classical compound Poisson model. In the present paper, the Bayesian robustness of this new model is examined and found to be much more robust than in the classical model in Gómez et al. (Insur Math Econ 31:105–113, 2002). For the present study, the moment conditions on the prior distribution are required. Examples, with real data, are given to illustrate our ideas under the net and exponential premium principles.