arXiv subjects

Gauss M. Cordeiro

Publications and source records attributed to Gauss M. Cordeiro.

17 recordsLinked to original sources

arXiv2025

The modified odd Burr XII-G family of distributions: Properties and Applications

The modified odd Burr XII-G family is developed, capable of incorporating bimodal and bathtub shapes in its baseline distributions, with properties derived from the exponentiated-G class. A regression model is developed within this family. The parameters are estimated by maximum likelihood, and simulations are performed to verify their consistency. The usefulness of the proposals is demonstrated by means of three real data sets.

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arXiv2025

The generalized Marshall-Olkin Lomax distribution with applications to AIDS and COVID-19 data

The generalized Marshall-Olkin Lomax distribution is introduced, and its properties are easily obtained from those of the Lomax distribution. A regression model for censored data is proposed. The parameters are estimated through maximum likelihood, and consistency is verified by simulations. Three real datasets are selected to illustrate the superiority of the new models compared to those from two well-known classes.

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arXiv2022

An extended Rayleigh model: Properties, regression and COVID-19 application

We define a four-parameter extended Rayleigh distribution, and obtain several mathematical properties including a stochastic representation. We construct a regression from the new distribution. The estimation is done by maximum likelihood. The utility of the new models is proved in two real applications.

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arXiv2022

New results and regression model for the exponentiated odd log-logistic Weibull family of distributions with applications

We obtain new mathematical properties of the exponentiated odd log-logistic family of distributions, and of its special case named the exponentiated odd log-logistic Weibull, and its log transformed. A new location and scale regression model is constructed, and some simulations are carried out to verify the behavior of the maximum likelihood estimators, and of the modified deviance-based residuals. The methodology is applied to the Japanese-Brazilian emigration data.

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arXiv2020

An introduction to Bent Jorgensen's ideas

We briefly expose some key aspects of the theory and use of dispersion models, for which Bent Jorgensen played a crucial role as a driving force and an inspiration source. Starting with the general notion of dispersion models, built using minimalistic mathematical assumptions, we specialize in two classes of families of distributions with different statistical flavors: exponential dispersion and proper dispersion models. The construction of dispersion models involves the solution of integral equations that are, in general, untractable. These difficulties disappear when a more mathematical structure is assumed: it reduces to the calculation of a moment generating function or of a Riemann-Stieltjes integral for the exponential dispersion and the proper dispersion models, respectively. A new technique for constructing dispersion models based on characteristic functions is introduced turning the integral equations above into a tractable convolution equation and yielding examples of dispersion models that are neither proper dispersion nor exponential dispersion models. A corollary is that the cardinality of regular and non-regular dispersion models are both large. Some selected applications are discussed including exponential families non-linear models (for which generalized linear models are particular cases) and several models for clustered and dependent data based on a latent Levy process.

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arXiv2012

A new class of fatigue life distributions

In this paper, we introduce the Birnbaum-Saunders power series class of distributions which is obtained by compounding Birnbaum-Saunders and power series distributions. The new class of distributions has as a particular case the two-parameter Birnbaum-Saunders distribution. The hazard rate function of the proposed class can be increasing and upside-down bathtub shaped. We provide important mathematical properties such as moments, order statistics, estimation of the parameters and inference for large sample. Three special cases of the new class are investigated with some details. We illustrate the usefulness of the new distributions by means of two applications to real data sets.

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arXiv2012

The Kumaraswamy Pareto distribution

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 (Gupta et al. [12]) 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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arXiv2012

The compound class of extended Weibull power series distributions

In this paper, we introduce a new class of distributions which is obtained by compounding the extended Weibull and power series distributions. The compounding procedure follows the same set-up carried out by Adamidis and Loukas (1998) and defines at least new 68 sub-models. This class includes some well-known mixing distributions, such as the Weibull power series (Morais and Barreto-Souza, 2010) and exponential power series (Chahkandi and Ganjali, 2009) distributions. Some mathematical properties of the new class are studied including 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 an EM algorithm is proposed for computing the estimates. Special distributions are investigated in some detail. An application to a real data set is given to show the flexibility and potentiality of the new class of distributions.

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arXiv2010

A New Generalized Kumaraswamy Distribution

A new five-parameter continuous distribution which generalizes the Kumaraswamy and the beta distributions as well as some other well-known distributions is proposed and studied. The model has as special cases new four- and three-parameter distributions on the standard unit interval. Moments, mean deviations, Rényi's entropy and the moments of order statistics are obtained for the new generalized Kumaraswamy distribution. The score function is given and estimation is performed by maximum likelihood. Hypothesis testing is also discussed. A data set is used to illustrate an application of the proposed distribution.

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arXiv2010

Skewness of maximum likelihood estimators in dispersion models

We introduce the dispersion models with a regression structure to extend the generalized linear models, the exponential family nonlinear models (Cordeiro and Paula, 1989) and the proper dispersion models (Jørgensen, 1997a). We provide a matrix expression for the skewness of the maximum likelihood estimators of the regression parameters in dispersion models. The formula is suitable for computer implementation and can be applied for several important submodels discussed in the literature. Expressions for the skewness of the maximum likelihood estimators of the precision and dispersion parameters are also derived. In particular, our results extend previous formulas obtained by Cordeiro and Cordeiro (2001) and Cavalcanti et al. (2009). A simulation study is perfomed to show the practice importance of our results.

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arXiv2009

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [1991, A log-linear model for the Birnbaum-Saunders distribution, Technometrics, 33, 51-60]. We discuss maximum likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. We also give an application to a real fatigue data set.

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arXiv2008

The Weibull-Geometric distribution

In this paper we introduce, for the first time, the Weibull-Geometric distribution which generalizes the exponential-geometric distribution proposed by Adamidis and Loukas (1998). The hazard function of the last distribution is monotone decreasing but the hazard function of the new distribution can take more general forms. Unlike the Weibull distribution, the proposed distribution is useful for modeling unimodal failure rates. We derive the cumulative distribution and hazard functions, the density of the order statistics and calculate expressions for its moments and for the moments of the order statistics. We give expressions for the Rényi and Shannon entropies. The maximum likelihood estimation procedure is discussed and an algorithm EM (Dempster et al., 1977; McLachlan and Krishnan, 1997) is provided for estimating the parameters. We obtain the information matrix and discuss inference. Applications to real data sets are given to show the flexibility and potentiality of the proposed distribution.

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arXiv2008

Asymptotic tail properties of the distributions in the class of dispersion models

The class of dispersion models introduced by Jørgensen (1997b) covers many known distributions such as the normal, Student t, gamma, inverse Gaussian, hyperbola, von-Mises, among others. We study the small dispersion asymptotic (Jørgensen, 1987b) behavior of the probability density functions of dispersion models which satisfy the uniformly convergent saddlepoint approximation. Our results extend those obtained by Finner et al. (2008).

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arXiv2008

Explicit expressions for moments of the beta Weibull distribution

The beta Weibull distribution was introduced by Famoye et al. (2005) and studied by these authors. However, they do not give explicit expressions for the moments. We now derive explicit closed form expressions for the cumulative distribution function and for the moments of this distribution. We also give an asymptotic expansion for the moment generating function. Further, we discuss maximum likelihood estimation and provide formulae for the elements of the Fisher information matrix. We also demonstrate the usefulness of this distribution on a real data set.

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arXiv2008

Some results for beta Fréchet distribution

Nadarajah and Gupta (2004) introduced the beta Fréchet (BF) distribution, which is a generalization of the exponentiated Fréchet (EF) and Fréchet distributions, and obtained the probability density and cumulative distribution functions. However, they do not investigated its moments and the order statistics. In this paper the BF density function and the density function of the order statistics are expressed as linear combinations of Fréchet density functions. This is important to obtain some mathematical properties of the BF distribution in terms of the corresponding properties of the Fréchet distribution. We derive explicit expansions for the ordinary moments and L-moments and obtain the order statistics and their moments. We also discuss maximum likelihood estimation and calculate the information matrix which was not known. The information matrix is easily numerically determined. Two applications to real data sets are given to illustrate the potentiality of this distribution.

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arXiv2008

The distribution of Pearson residuals in generalized linear models

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size. We define corrected Pearson residuals for these models that, to this order of approximation, have exactly the same distribution of the true Pearson residuals. Applications for important generalized linear models are provided and simulation results for a gamma model illustrate the usefulness of the corrected Pearson residuals.

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arXiv2008

The Beta Generalized Exponential Distribution

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the $r$th moment thus generalizing some results in the literature. Expressions for the density, moment generating function and $r$th moment of the order statistics also are obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix. We observe in one application to real data set that this model is quite flexible and can be used quite effectively in analyzing positive data in place of the beta exponential and generalized exponential distributions.

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