9 citations · 24 across the 54 of their papers we have counts for
56 papers
Exact finite-sample bias, variance, and MSE of normalized scale-invariant inequality indices under Gamma mixture models
Roberto Vila, Felipe Quintino
We study the finite-sample properties of estimators of a broad class of normalized scale-invariant inequality indices (NSIIs) under finite Gamma mixture models. The class includes…
Characterizations of independence between order statistics and rank indicators
Roberto Vila, Frederico Almeida
We study the independence between an order statistic and its corresponding rank indicator for independent nonnegative random variables. A general characterization is established th…
Conditional copula representations and extremal bounds for multivariate statistical functionals
Roberto Vila, Cira E G Otiniano, Carolyne Brito +1
In this paper, we derive a conditional copula representation for expectations of the form , where is a random vector with arbitrary…
Income inequality estimation with gamma mixtures
Roberto Vila, Helton Saulo, Felipe Quintino
This paper studies the estimation of the th Gini index under finite mixtures of gamma distributions. We derive closed-form expressions for the th Gini index and for the expec…
Unbiased estimation of normalized scale-invariant indices under the Gamma distribution
Roberto Vila, Helton Saulo, Felipe Quintino
We introduce a broad class of normalized scale-invariant indices (NSIIs) generated by measurable symmetric homogeneous functions and encompassing several well-known measures, inclu…
Length-biased Birnbaum-Saunders quantile regression with application to water evaporation
Helton Saulo, Tailine Nonato, Roberto Vila
Length-biased distributions arise naturally in environmental, reliability, and economic studies where the sampling mechanism favors larger observational units. In this paper, we pr…
Quantile autoregressive moving average models for ratio-based bounded time series
Helton Saulo, Roberto Vila, Filidor Vilca
This paper proposes the quantile unit-log-symmetric autoregressive moving average (QULS--ARMA) model for bounded time series on the open unit interval . The model extends th…
The arithmetic-harmonic inequality index: Theory, inference, and finite-sample analysis
Roberto Vila, Helton Saulo
We investigate the arithmetic-harmonic inequality (AHI) index, a bounded and scale-invariant measure of dispersion for positive random variables, defined through the interplay betw…
Unifying the Hoover and Gini indices: Analytical, bias, and computational aspects
Roberto Vila, Helton Saulo, Felipe Quintino
We propose a new family of inequality indices that bridges the Hoover index and the Gini coefficient. The measure is defined as the normalized expected absolute value of a convex c…
Modeling double bounded data based on correlated gamma random variables
Roberto Vila, Felipe Quintino, Marcelo Bourguignon
Many types of bounded data defined on the unit interval arise naturally as ratios of the form . In the existing literature, the main statistical models proposed for this…
On the bias of the Hoover index estimator: Results for the gamma distribution
Roberto Vila, Helton Saulo
The Hoover index is a widely used measure of inequality with an intuitive interpretation, yet little is known about the finite-sample properties of its empirical estimator. In this…
Bias analysis of a linear order-statistic inequality index estimator: Unbiasedness under gamma populations
Roberto Vila, Helton Saulo
This paper studies a class of rank-based inequality measures built from linear combinations of expected order statistics. The proposed framework unifies several well-known indices,…
On the bias of the Gini estimator: Poisson and geometric cases, a characterization of the gamma family, and unbiasedness under gamma distributions
Roberto Vila, Helton Saulo
In this paper, we derive a general representation for the expectation of the Gini coefficient estimator in terms of the Laplace transform of the underlying distribution, together w…
Closed-form parameter estimation for the bivariate gamma distribution: New approaches
Roberto Vila, Helton Saulo
We propose new closed-form estimators for the parameters of McKay's bivariate gamma distribution by exploiting monotone transformations of the likelihood equations. As a special ca…
A transformed-score approach to closed-form and one-step efficient estimation for the beta distribution
Roberto Vila, Helton Saulo, Felipe Quintino +1
Power transformations of beta random variables produce unbiased estimating equations from transformed-model likelihood scores. This construction clarifies the connection between mo…
Two Tunable Gini-Type Measures with U-Statistic Estimation: Theory, Simulation, and an Empirical Application to GDP per Capita in the Americas
Roberto Vila, Helton Saulo
We introduce two families of inequality measures, and , that converge to the classical Gini coefficient as . The tuning parameters and regulate…
On classes of distributions on the unit interval: structural properties and application to inequality data
Roberto Vila, Helton Saulo, Poliana Matos +1
Probability distributions defined on the unit interval are widely used in fields ranging from econometrics to reliability studies. Traditional models such as the beta and Kumaraswa…
Bias in estimating Theil, Atkinson, and dispersion indices for gamma mixture populations
Jackson Assis, Roberto Vila, Helton Saulo
This paper examines the finite-sample bias of estimators for the Theil and Atkinson indices, as well as for the variance-to-mean ratio (VMR), under the assumption that the populati…
Unbiased estimation in new Gini index extensions under gamma distributions, with application to real income data
Roberto Vila, Helton Saulo
In this paper, we introduce two flexible extensions of the classical Gini index, referred to as the extended lower and upper Gini indices. The proposed measures are based on the di…
Closed-form solutions for parameter estimation in exponential families based on maximum a posteriori equations
Roberto Vila, Helton Saulo, Eduardo Nakano
In this paper, we derive closed-form estimators for the parameters of certain exponential family distributions through the maximum a posteriori (MAP) equations. A Monte Carlo simul…
An unbiased estimator of a novel extended Gini index for gamma distributed populations
Roberto Vila, Helton Saulo
In this paper, we introduce a novel flexible Gini index, referred to as the extended Gini index, which is defined through ordered differences between the th and th order stat…
The th Gini index estimator: Unbiasedness for gamma populations
Roberto Vila, Helton Saulo
This paper establishes the theoretical result that the sample th Gini index is an unbiased estimator of the population th Gini index, introduced by Gavilan-Ruiz (2024), for g…
Closed-form formulas for the biases of the Theil and Atkinson index estimators in Gamma distributed populations
Roberto Vila, Helton Saulo
This paper presents an analysis of the Theil and Atkinson index estimators for gamma populations, highlighting the presence of bias in both cases. Theoretical expressions for the b…
On the bias of the Gini coefficient estimator for zero-truncated Poisson distributions
Roberto Vila, Helton Saulo
This paper analyzes the Gini coefficient estimator for zero-truncated Poisson populations, revealing the presence of bias, and provides a mathematical expression for the bias, alon…