Gauss Cordeiro

Universidade Federal de Pernambuco, Statistics, Faculty Member

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Papers by Gauss Cordeiro

Generalized Statistical Distributions

Springer handbooks, Feb 24, 2012

Explaining COVID-19 mortality rates in the first wave in Europe

Model Assisted Statistics and Applications

The beta regression has been received considerable attention in the last decade because of its ap... more The beta regression has been received considerable attention in the last decade because of its applications to proportional data in several fields. We study the variability of coronavirus death rates in the first wave of twenty European countries using the beta regression with two systematic components for the mean and dispersion parameters. We prove empirically that the population density, proportion of urban population, hospital beds per 100 thousand and running time explain the variability of the COVID-19 death rates in the first wave of these countries.

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The Extended Dagum Distribution: Properties and Application

Journal of Data Science

We study a new five-parameter model called the extended Dagum distribution. The proposed model co... more We study a new five-parameter model called the extended Dagum distribution. The proposed model contains as special cases the log-logistic and Burr III distributions, among others. We derive the moments, generating and quantile functions, mean deviations and Bonferroni, Lorenz and Zenga curves. We obtain the density function of the order statistics. The parameters are estimated by the method of maximum likelihood. The observed information matrix is determined. An application to real data illustrates the importance of the new model.

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The Logit Exponentiated Power Exponential Regression with Applications

Annals of Data Science, 2021

A new extended mixture normal distribution

Mathematical Communications, 2017

The normal distribution is the most important model in statistics for analysisof continuous data.... more The normal distribution is the most important model in statistics for analysisof continuous data. We propose a new distribution, called the extended mixture normaldistribution, based on a linear mixture model. We obtain explicit expressions for theordinary and incomplete moments, generating and quantile functions, mean deviations andtwo measures of entropy. The method of maximum likelihood and Bayesian are adopted toestimate the model parameters. The proposed distribution can provide better fits to realdata than the normal and other classical distributions as shown by means of one application.

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A novel generalized odd log-logistic Maxwell-based regression with application to microbiology

Applied Mathematical Modelling, 2021

Abstract The presence of bimodality, heteroskedasticity, zero-inflation and nonlinear effects in ... more Abstract The presence of bimodality, heteroskedasticity, zero-inflation and nonlinear effects in covariables is common in several real data applications. In this context, new regressions are proposed for data with all these characteristics. The estimation of parameters follows the maximum likelihood method. For different fixed parameters, sample sizes and percentages of zeros, various simulations are performed to assess the behavior of the estimators. Quantile residuals are defined to evaluate the assumptions of the proposed regression. Its usefulness is illustrated by an experiment conducted to assess the soil microbiology in a sugarcane field.

Extension of generalized integro-exponential function and its application in study of Chen distribution

Applicable Analysis and Discrete Mathematics, 2017

In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical p... more In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical properties moments, quantile and generating functions, among others. In this article, we derive a power series expansion for newly introduced real upper parameter generalized integro-exponential function Eps(z) extending certain Milgram's findings. By our novel results we derive closed-form expressions for the moments, generating function, R?nyi entropy and power series for the quantile function of the Chen distribution.

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A flexible bimodal model with long-term survivors and different regression structures

Communications in Statistics - Simulation and Computation, 2018

The cure fraction models are useful to model lifetime data with long-term survivors. In this pape... more The cure fraction models are useful to model lifetime data with long-term survivors. In this paper, we introduce a flexible cure rate survival model where the model parameters are related to covariates in different regression structures. The regression model allows to model jointly the location, scale and shape effects. The maximum likelihood method is employed to estimate the model parameters. We provide Monte Carlo simulation experiments to verify the performance of the maximum likelihood estimates for different sample sizes and cure rate percentages. Furthermore, some diagnostic measures to assess departures from model assumptions as well as to detect outlying observations are also considered. Finally, applications to real data are presented to show the usefulness of the new cure rate model.

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Heteroscedastic log-exponentiated Weibull regression model

Journal of Applied Statistics, 2017

ABSTRACT We introduce a new class of heteroscedastic log-exponentiated Weibull (LEW) regression m... more ABSTRACT We introduce a new class of heteroscedastic log-exponentiated Weibull (LEW) regression models. The class of regression models can be applied to censored data and be used more effectively in survival analysis. Maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model is investigated. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the heteroscedastic LEW regression model. The normal curvatures for studying local influence are derived under various perturbation schemes. An empirical application to a real data set is provided to illustrate the usefulness of the new class of heteroscedastic regression models.

The odd Birnbaum–Saunders regression model with applications to lifetime data

Journal of Statistical Theory and Practice, 2016

We introduce a new three-parameter lifetime model called the odd Birnbaum-Saunders distribution. ... more We introduce a new three-parameter lifetime model called the odd Birnbaum-Saunders distribution. We construct an extended regression model based on the logarithm of the new distribution, which can be applied to censored data and be more effective in analyzing real data. Maximum likelihood estimation of the model parameters of the new regression model is discussed for complete and censored samples. A modified deviance residual is proposed to assess departures from the log-odd Birnbaum-Saunders error assumption and to detect outlying observations. Real data sets are analyzed for illustrative purposes.

Extended arcsine distribution to proportional data: Properties and applications

Studia Scientiarum Mathematicarum Hungarica, 2016

We propose a new two-parameter continuous model called the extended arcsine distribution restrict... more We propose a new two-parameter continuous model called the extended arcsine distribution restricted to the unit interval. It is a very competitive model to the beta and Kumaraswamy distributions for modeling percentages, rates, fractions and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for the ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating and quantile functions, Shannon entropy and order statistics. Maximum likelihood is used to estimate the model parameters and the expected information matrix is determined. We demonstrate by means of two applications to proportional data that it can give consistently a better fit than other important statistical models.

The Beta-Half-Cauchy Distribution

Journal of Probability and Statistics, 2011

On the basis of the half-Cauchy distribution, we propose the called beta-half-Cauchy distribution... more On the basis of the half-Cauchy distribution, we propose the called beta-half-Cauchy distribution for modeling lifetime data. Various explicit expressions for its moments, generating and quantile functions, mean deviations, and density function of the order statistics and their moments are provided. The parameters of the new model are estimated by maximum likelihood, and the observed information matrix is derived. An application to lifetime real data shows that it can yield a better fit than three- and two-parameter Birnbaum-Saunders, gamma, and Weibull models.

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Recent Advances in Univariate and Multivariate Models

Journal of Probability and Statistics, 2013

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An extended Lomax distribution

Statistics, 2013

A new five-parameter continuous distribution, the so-called McDonald Lomax distribution, that ext... more A new five-parameter continuous distribution, the so-called McDonald Lomax distribution, that extends the Lomax distribution and some other distributions is proposed and studied. The model has as special submodels new four-and three-parameter distributions. Various structural properties of the new distribution are derived, including expansions for the density function, explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The score function is derived and the estimation is performed by maximum likelihood. We also obtain the observed information matrix. An application illustrates the usefulness of the proposed model.

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The McDonald arcsine distribution: a new model to proportional data

Statistics, 2012

ABSTRACT We propose a new three-parameter continuous model called the McDonald arcsine distributi... more ABSTRACT We propose a new three-parameter continuous model called the McDonald arcsine distribution, which is a very competitive model to the beta, beta type I and Kumaraswamy distributions for modelling rates and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for the density function, moments, generating and quantile functions, mean deviations, two probability measures based on the Bonferroni and Lorenz curves, Shannon entropy, Rényi entropy and cumulative residual entropy. Maximum likelihood is used to estimate the model parameters and the expected information matrix is determined. An application of the proposed model to real data shows that it can give consistently a better fit than other important statistical models.

The beta Laplace distribution

Statistics & Probability Letters, 2011

The Laplace distribution is one of the earliest distributions in probability theory. For the firs... more The Laplace distribution is one of the earliest distributions in probability theory. For the first time, based on this distribution, we propose the so-called beta Laplace distribution, which extends the Laplace distribution. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters and derive the observed information matrix. The usefulness of the new model is illustrated by means of a real data set.

Asymptotic skewness in Birnbaum–Saunders nonlinear regression models

Statistics & Probability Letters, 2010

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetim... more The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n−1/2, where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum–Saunders nonlinear

On the Marshall–Olkin extended Weibull distribution

Statistical Papers, 2012

ABSTRACT We study some mathematical properties of the Marshall–Olkin extended Weibull distributio... more ABSTRACT We study some mathematical properties of the Marshall–Olkin extended Weibull distribution introduced by Marshall and Olkin (Biometrika 84:641–652, 1997). We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, reliability and Rényi entropy. We determine the moments of the order statistics. We also discuss the estimation of the model parameters by maximum likelihood and obtain the observed information matrix. We provide an application to real data which illustrates the usefulness of the model.

The Marshall–Olkin Family of Distributions: Mathematical Properties and New Models

Journal of Statistical Theory and Practice, 2014

ABSTRACT Marshall and Olkin (1997) introduced a general method for obtaining more flexible distri... more ABSTRACT Marshall and Olkin (1997) introduced a general method for obtaining more flexible distributions by adding a new parameter to an existing one, called the Marshall–Olkin family of distributions. In this article, we provide a comprehensive treatment of general mathematical and statistical properties of this family of distributions. Moreover, we propose three new distributions on the basis of the Marshall–Olkin scheme. We discuss maximum likelihood estimation with censored data and provide the observed information matrix. The usefulness of the new family is illustrated by means of an application to real data.

The Kumaraswamy Pareto distribution

Journal of Statistical Theory and Applications, 2013

The modeling and analysis of lifetimes is an important aspect of statistical work in a wide varie... more The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the called Kumaraswamy Pareto distribution, is introduced and studied. The new distribution can have a decreasing and upside-down bathtub failure rate function depending on the values of its parameters. It includes as special sub-models the Pareto and exponentiated Pareto distributions. Some structural properties of the proposed distribution are studied including explicit expressions for the moments and generating function. We provide the density function of the order statistics and obtain their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. A real data set is used to compare the new model with widely known distributions.

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Gauss Cordeiro

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