arXiv subjects

Felipe Quintino

Publications and source records attributed to Felipe Quintino.

9 recordsLinked to original sources

arXiv2026

Income inequality estimation with gamma mixtures

This paper studies the estimation of the $m$th Gini index under finite mixtures of gamma distributions. We derive closed-form expressions for the $m$th Gini index and for the expectation and bias of its non-parametric U-statistic estimator, extending previous results for both single gamma populations and gamma mixture models. We further establish the asymptotic properties of the estimator for gamma mixtures sharing a common rate parameter, including an asymptotic lower bound for the bias, asymptotic unbiasedness, strong consistency, and asymptotic normality. Although these theoretical results require a common rate parameter, a Monte Carlo study also investigates the estimator under mixtures with different rates and compares its performance with bias-corrected and parametric estimators. Finally, the proposed methodology is illustrated through the analysis of an income dataset.

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arXiv2026

Unbiased estimation of normalized scale-invariant indices under the gamma distribution

We introduce a broad class of normalized scale-invariant indices (NPRIs) generated by homogeneous functions and encompassing several well-known measures, including the Gini coefficient, generalized Gini indices, entropy-based measures, and variability indices. Explicit expressions are obtained for these indices under gamma populations. Exploiting the independence between the total sum and the associated Dirichlet proportions, we derive a simple unbiased estimator based on a U-statistic. The resulting estimator is shown to be unbiased for any NPRI when the underlying population follows a gamma distribution. Several examples are provided to illustrate the general theory. A Monte Carlo simulation study is carried out that shows the good performance of the unbiased estimator in several scenarios of index choices. We also present a simulation study that goes beyond the established theory by examining the estimator's applicability in settings characterized by a generalized gamma distribution. We evaluate the effectiveness of the NPRIs and their estimates in modeling a real-world dataset related to gross domestic product per capita in the Americas.

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arXiv2026

Unifying the Hoover and Gini indices: Analytical, bias, and computational aspects

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 combination of deviations from the mean and pairwise differences, providing a continuous interpolation between these two classical indices. We establish key theoretical properties, including scale invariance, boundedness, continuity, and compliance with the Pigou-Dalton transfer principle. Analytical representations are derived, allowing explicit evaluation under gamma distributions and leading to closed-form expressions involving incomplete gamma functions. From a statistical perspective, we study the plug-in estimator, obtaining a general expression for its expectation and explicit formulas for its bias under gamma populations. Simulation results indicate good finite-sample performance, with decreasing bias and mean squared error as the sample size increases. An empirical application to GDP per capita data illustrates the practical usefulness of the proposed index as a flexible tool for inequality analysis.

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arXiv2026

Modeling double bounded data based on correlated gamma random variables

Many types of bounded data defined on the unit interval arise naturally as ratios of the form $X/(X + Y)$. In the existing literature, the main statistical models proposed for this type of bounded data typically based on the assumption that the random variables $X$ and $Y$ are independent. However, this assumption is often unrealistic in practical applications, where $X$ and $Y$ tend to be correlated due to shared underlying mechanisms or common sources of variability. In this paper, we overcome such limitations and propose a model in which the marginal distributions of the two components are linked by a copula, leading to a more flexible and realistic representation of unit-interval data. In particular, in the proposed model, $X$ and $Y$ are dependent gamma random variables whose joint distribution is specified via Morgenstern's bivariate distribution}, allowing for positive and negative correlations between the components. The mathematical properties and practical applications are rigorously investigated. The resulting distribution exhibits a wide range of shapes, accommodating different degrees of skewness and, for some parameter configurations, more complex density structures. A Monte Carlo simulation study is carried out that shows the good performance of the maximum likelihood estimator in several scenarios of parameter choices. The potential and limitations of efficient likelihood-based computations are also discussed. We evaluate the effectiveness of the new model and its estimates in modeling real-world datasets related to economics.

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arXiv2025

A transformed-score approach to closed-form and one-step efficient estimation for the beta distribution

Power transformations of beta random variables produce unbiased estimating equations from transformed-model likelihood scores. This construction clarifies the connection between moment-type and likelihood-based estimating equations, recovers recent closed-form estimators for the beta shape parameters, and yields a new family indexed by a scalar transformation parameter $r$. For each fixed admissible $r$, we establish strong consistency and joint asymptotic normality. We also show that likelihood-guided selection over a prespecified finite grid preserves root-$n$ consistency and use one Fisher-scoring update to obtain an asymptotically efficient estimator. A Monte Carlo study with 1000 replications compares numerical maximum likelihood, two existing closed-form procedures, the proposed likelihood-selected closed-form estimator, and its one-step refinement across nine parameter configurations and four sample sizes. All procedures are evaluated on the same simulated samples within each replication. The selected closed-form estimator closely tracks maximum likelihood, while the one-step refinement is nearly indistinguishable from it for moderate sample sizes. Finally, the methods are illustrated descriptively using the proportions of municipal area devoted to crops and pasture in the 15 municipalities of Roraima, Brazil.

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arXiv2025

A novel unit-asymmetric distribution based on correlated Fréchet random variables

In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type $W=X_1/(X_1+X_2)$, where $(X_1, X_2)^\top$ follows a bivariate extreme distribution with Fréchet margins, that is, $X_1$ and $X_2$ are two correlated Fréchet random variables. Some mathematical properties such as identifiability, symmetry, stochastic representation, characterization as a ratio, moments, stress-strength probability, quantiles, and the maximum likelihood method are rigorously analyzed. Two applications of the ratio distribution are discussed.

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arXiv2024

A new unit-bimodal distribution based on correlated Birnbaum-Saunders random variables

In this paper, we propose a new distribution over the unit interval which can be characterized as a ratio of the type $Z=Y/(X+Y)$ where $X$ and $Y$ are two correlated Birnbaum-Saunders random variables. The density of $Z$ may be unimodal or bimodal. Simple expressions for the cumulative distribution function, moment-generating function and moments are obtained. Moreover, the stress-strength probability between $X$ and $Y$ is calculated explicitly in the symmetric case, that is, when the respective scale parameters are equal. Two applications of the ratio distribution are discussed.

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arXiv2024

Family of multivariate extended skew-elliptical distributions: Statistical properties, inference and application

In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties, including the characterization of the density function for various distribution types, as well as other key aspects such as identifiability, quantiles, stochastic representation, conditional and marginal distributions, moments, Kullback-Leibler Divergence, and parameter estimation. A Monte Carlo simulation study is performed for examining the performance of the developed parameter estimation method. Finally, the proposed models are used to analyze socioeconomic data.

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arXiv2022

A General Class of Trimodal Distributions: Properties and Inference

The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions that have up to three modes. Trimodality itself is achieved by applying a proper transformation to density function of certain continuous probability distributions. At first, we obtain preliminary results for an arbitratry density function $g(x)$ and, next, we focus on the Gaussian case, studying trimodal Gaussian model more deeply. The Gaussian distribution is applied to produce the trimodal form of Gaussian known as normal distribution. The tractability of analytical expression of normal distribution, and properties of the trimodal normal distribution are important reasons why we choose normal distribution. Furthermore, the existing distributions should be improved to be capable of modelling efficiently when there exists a trimodal form in a data set. After new density function is proposed, estimating its parameters is important. Since Mathematica 12.0 software has optimization tools and important modelling techniques, computational steps are performed by using this software. The bootstrapped form of real data sets are applied to show the modelling ability of the proposed distribution when real data sets show trimodality.

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