Navegando por Autor "Cordeiro, Gauss M."
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Artigo General results for the transmuted Family of distributions and new models(Journal of Probability and Statistics, 2016) Bourguignon, Marcelo; Ghosh, Indranil; Cordeiro, Gauss M.The transmuted family of distributions has been receiving increased attention over the last few years. For a baseline G distribution, we derive a simple representation for the transmuted-G family density function as a linear mixture of the G and exponentiated-G densities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, R´enyi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.Artigo Improved likelihood-based inference in Birnbaum–Saunders nonlinear regression models(Applied Mathematical Modelling, 2016-04) Lemonte, Artur J.; Cordeiro, Gauss M.; Moreno-Arenas, GermánWe address the issue of performing testing inference in Birnbaum–Saunders nonlinear re- gression models when the sample size is small. The likelihood ratio, Wald and score statis- tics provide the basis for testing inference on the parameters in this class of models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test statistics. We derive a general Bartlett-type correction in matrix notation for the score test, which reduces the size distor- tion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald and score tests, and with the Bartlett-corrected likelihood ratio test, and bootstrap- corrected tests. Our simulation results suggest that the proposed corrected test can be an interesting alternative to other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.Artigo A new compounding family of distributions: the generalized gamma power series distributions(Journal of Computational and Applied Mathematics, 2016-01) Silva, Rodrigo B.; Bourguignon, Marcelo; Cordeiro, Gauss M.We propose a new four-parameter family of distributions by compounding the generalized gamma and power series distributions. The compounding procedure is based on the work by Marshall and Olkin (1997) and defines 76 sub-models. Further, it includes as special models the Weibull power series and exponential power series distributions. Some mathematical properties of the new family are studied including moments and generating function. Three special models are investigated in detail. Maximum likelihood estimation of the unknown parameters for complete sample is discussed. Two applications of the new models to real data are performed for illustrative purposes.Artigo The beta odd log-logistic generalized family of distributions(Hacettepe Journal of Mathematics and Statistics, 2015) Cordeiro, Gauss M.; Alizadeh, Morad; Tahir, M. H.; Mansoor, M.; Bourguignon, Marcelo; Hamedani, G. G.We introduce a new family of continuous models called the beta odd log-logistic generalized family of distributions. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, reversed-J, unimodal and bimodal shaped, and has constant, increasing, decreasing, upside-down bathtub and J-shaped hazard rates. Five special models are discussed. We obtain explicit expressions for the moments, quantile function, moment generating function, mean deviations, order statistics, R´enyi entropy and Shannon entropy. We discuss simulation issues, estimation by the method of maximum likelihood, and the method of minimum spacing distance estimator. We illustrate the importance of the family by means of two applications to real data sets.Artigo The exponentiated generalized extended exponential distribution(Journal of Data Science, 2016) Andrade, Thiago A. N. de; Bourguignon, Marcelo; Cordeiro, Gauss M.We introduce and study a new four-parameter lifetime model named the exponentiated generalized extended exponential distribution. The proposed model has the advantage of including as special cases the exponential and exponentiated exponential distributions, among others, and its hazard function can take the classic shapes: bathtub, inverted bathtub, increasing, decreasing and constant, among others. We derive some mathematical properties of the new model such as a representation for the density function as a double mixture of Erlang densities, explicit expressions for the quantile function, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R´enyi entropy, density of order statistics and reliability. We use the maximum likelihood method to estimate the model parameters. Two applications to real data illustrate the flexibility of the proposed model.Artigo The exponentiated generalized standardized half-logistic distribution(Canadian Center of Science and Education, 2017-05) Cordeiro, Gauss M.; Andrade, Thiago A. N. de; Bourguignon, Marcelo; Silva, Frank GomesWe study a new two-parameter lifetime model called the exponentiated generalized standardized half-logistic distribution, which extends the half-logistic pioneered by Balakrishnan in the eighties. We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, and order statistics. The model parameters are estimated by the maximum likelihood method. A simulation study reveals that the estimators have desirable properties such as small biases and variances even in moderate sample sizes. We prove empirically that the new distribution provides a better fit to a real data set than other competitive models.Artigo The gamma extended Weibull family of distributions(Journal of Statistical Theory and Applications, 2014-03) Nascimento, Abraão D. C.; Bourguignon, Marcelo; Zea, Luz M.; Santos-Neto, Manoel; Silva, Rodrigo B.; Cordeiro, Gauss M.We introduce a new family of distributions called the gamma extended Weibull family. The proposed family includes several well-known models as special cases and defines at least seventeen new special models. Structural properties of this family are studied. Additionally, the maximum likelihood method for estimating the model parameters is discussed. An application to real data illustrates the usefulness of the new family. The results provide evidence that the proposed family outperforms other classes of lifetime models.Artigo The gamma generalized pareto distribution with applications in survival analysis(International Journal of Statistics and Probability, 2017-05) Andrade, Thiago A. N. de; Fernandez, Luz Milena Zea; Silva, Frank Gomes; Cordeiro, Gauss M.We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R´enyientropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.Artigo The Marshall-Olkin extended Weibull family of distributions(Journal of Statistical Distributions and Applications, 2014) Santos-Neto, Manoel; Bourguignon, Marcelo; Zea, Luz M.; Nascimento, Abraão DC; Cordeiro, Gauss M.We introduce a new class of models called the Marshall-Olkin extended Weibull family of distributions based on the work by Marshall and Olkin (Biometrika 84:641–652, 1997). The proposed family includes as special cases several models studied in the literature such as the Marshall-Olkin Weibull, Marshall-Olkin Lomax, Marshal-Olkin Fréchet and Marshall-Olkin Burr XII distributions, among others. It defines at least twenty-one special models and thirteen of them are new ones. We study some of its structural properties including moments, generating function, mean deviations and entropy. We obtain the density function of the order statistics and their moments. Special distributions are investigated in some details. We derive two classes of entropy and one class of divergence measures which can be interpreted as new goodness-of-fit quantities. The method of maximum likelihood for estimating the model parameters is discussed for uncensored and multi-censored data. We perform a simulation study using Markov Chain Monte Carlo method in order to establish the accuracy of these estimators. The usefulness of the new family is illustrated by means of two real data sets.