The aim of this paper is to assess the evolution of multidimensional inequality in well-being using Lorenz curves. Closed expressions for the bivariate Lorenz curve defined by Arnold (1983) are given. We assume a relevant type of models based on the class of distributions with given marginals described by Sarmanov and Lee (Lee, 1996; Sarmanov, 1966). This specification of the bivariate Lorenz c...

In this paper, we derive recurrence relations for cumulative distribution functions (cdf’s) of bivariate t and extended skew-t distributions. These recurrence relations are over ν (the degrees of freedom), and starting from the known results for ν = 1 and ν = 2, they will allow for the recursive evaluation of the distribution function for any other positive integral value of ν. Then, we conside...

Abstract A procedure is presented for using the bivariate normal distribution to describe the joint distribution of storm peaks (maximum rainfall intensities) and amounts which are mutually correlated. The Box-Cox transformation method is used to normalize original marginal distributions of storm peaks and amounts regardless of the original forms of these distributions. The transformation param...

The local dependence function (LDF) describes changes in the correlation structure of continuous bivariate random variables along their range. Bivariate density functions with Beta marginals can be used to model jointly a wide variety of data with bounded outcomes in the (0,1) range, e.g. proportions. In this paper we obtain expressions for the LDF of bivariate densities constructed using three...

This paper deals with transportation polytopes in the probability simplex (that is, sets of categorical bivariate probability distributions with prescribed marginals). Information projections between such polytopes are studied, and a sufficient condition is described under which these mappings are homeomorphisms. 1. Preliminaries Let Γn denote the set of probability distributions with alphabet ...

Block (1975) extended bivariate exponential distributions (BVEDs) of Freund (1961) and Proschan and Sullo (1974) to multivariate case and called them as Generalized FreundWeinman's multivariate exponential distributions (MVEDs). In this paper, we obtain MLEs of the parameters and large sample test for testing independence and symmetry of k components in the generalized Freund-Weinman's MVEDs.

Correspondence analysis is a multivariate technique used to visualize categorical data, usually data in a two-way contingency table. Some extensions of correspondence analysis to a continuous bivariate distribution are presented, rstly from a canonical correlation analysis perspective and then from a continuous scaling perspective. These extensions are applied to the Farlie-Gumbel-Morgenstern (...

The Wiener index is analyzed for random recursive trees and random binary search trees in the uniform probabilistic models. We obtain the expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed-point equations. Covariances, asymptotic correlations, and bivariate ...

In this paper we discuss the representation of the joint probability density function of perfectly correlated continuous random variables, i.e., with correlation coefficients ρ=±1, by Dirac’s δ-function. We also show how this representation allows to define Dirac’s δ-function as the ratio between bivariate distributions and the marginal distribution in the limit ρ → ±1, whenever this limit exis...

In a Monte Carlo study, we compare ten bivariate location estimators as regards their closeness to the location parameter, accuracy and robustness. The behavior of the estimators is examined under various sampling situations determined by four sample sizes and fourteen underlying distributions. In addition to the arithmetic mean, five bivariate medians and four depth-based trimmed means are inv...