Navegando por Autor "Bourguignon, Marcelo"

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An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion
(Springer, 2017-04) Bourguignon, Marcelo; Weiss, Christian H.
We present a novel first-order nonnegative integer-valued autoregressive model for stationary count data processes with Bernoulli-geometric marginals based on a new type of generalized thinning operator. It can be used for modeling time series of counts with equidispersion, underdispersion and overdispersion. The main properties of the model are derived, such as probability generating function, moments, transition probabilities and zero probability. The maximum likelihood method is used for estimating the model parameters. The proposed model is fitted to time series of counts of iceberg orders and of cases of family violence illustrating its capabilities in challenging cases of overdispersed and equidispersed count data.
Combinação de modelos de previsão climática
(Universidade Federal do Rio Grande do Norte, 2018-06-14) Moura, Isabelle; Nunes, Marcus; Pinho, André; Bourguignon, Marcelo
A precipitação é uma das variáveis mais importantes para descrever o clima futuro, pois descreve qualquer tipo de fenômeno relacionado à queda de água do céu. Existem diversos modelos de simulação climática previsão da precipitação hoje. Os modelos adotados neste trabalho serão o BCC-CSM1.1, CCSM4, CESM1, CPC-NOAA, NorESM1-ME e MRI-CGCM3 em três regiões distintas Amazônia, Bacia do Rio da Prata e o Nordeste Brasileiro. São considerados três tipos de cenários diferentes: RCP 4.5, RCP 6.0 e RCP 8.5. Cenários possuem diferentes características em relação às variáveis de emissão de gases, concentração de gases de efeito estufa, e informações de tipo de cobertura terrestre. Estudos anteriores mostram que a combinação entre modelos torna a previsão mais precisa. Devido a isso, foram adotados dois métodos de combinação de modelos, chamados Random Forest e SVM (Support Vector Machine – Máquina de Vetores Suporte). A raíz do erro quadrático médio foi utilizada para a comparação entre os dois métodos, após essa comparação foi observado que os dois métodos conseguem fazer uma previsão aproximada dos valores reais, sendo o Random Forest tendo o menor erro quadrático médio em todos os diferentes tipos de cenários entre as regiões escolhidas.
Extended generalized extreme value distribution with applications in environmental data
(Journal of Mathematics and Statistics, 2015) Nascimento, Fernando; Bourguignon, Marcelo; Leão, Jeremias
In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory, which has wide applicability in several areas including hydrology, engineering, science, ecology and finance. In this paper, we propose three extensions of the GEV distribution that incorporate an additional parameter. These extensions are more flexible than the GEV distribution, i.e., the additional parameter introduces skewness and to vary tail weight. In these three cases, the GEV distribution is a particular case. The parameter estimation of these new distributions is done under the Bayesian paradigm, considering vague priors for the parameters. Simulation studies show the efficiency of the proposed models. Applications to river quotas and rainfall show that the generalizations can produce more efficient results than is the standard case with GEV distribution.
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.
A generalised NGINAR(1) process with inflated-parameter geometric counting series
(Australian and New Zeland Jounal of Statistics, 2017) Borges, Patrick; Bourguignon, Marcelo; Molinares, Fabio Fajardo
In this paper we propose a new stationary first-order non-negative integer valued autoregressive process with geometric marginals based on a generalised version of the negative binomial thinning operator. In this manner we obtain another process that we refer to as a generalised stationary integer-valued autoregressive process of the first order with geometric marginals. This new process will enable one to tackle the problem of overdispersion inherent in the analysis of integer-valued time series data, and contains the new geometric process as a particular case. In addition various properties of the new process, such as conditional distribution, autocorrelation structure and innovation structure, are derived. We discuss conditional maximum likelihood estimation of the model parameters. We evaluate the performance of the conditional maximum likelihood estimators by a Monte Carlo study. The proposed process is fitted to time series of number of weekly sales (economics) and weekly number of syphilis cases (medicine) illustrating its capabilities in challenging cases of highly overdispersed count data.
A geometric time series model with inflated-parameter Bernoulli counting series
(Statistics and Probability Letters, 2016-08) Borges, Patrick; Molinares, Fabio Fajardo; Bourguignon, Marcelo
In this paper, we propose a new stationary first-order non-negative integer valued autoregressive [INAR(1)] process with geometric marginals based on a modified version of the binomial thinning operator. This new process will enable one to tackle the problem of overdispersion inherent in the analysis of integer-valued time series data that may arise due to the presence of some correlation between underlying events, heterogeneity of the population, excess to zeros, among others. In addition, it includes as special cases the geometric INAR(1) [GINAR(1)] (Alzaid and Al-Osh, 1988) and new geometric [NGINAR(1)] (Ristić et al., 2009) processes, making it be very useful in discriminating between nested models. The innovation structure of the new process is very simple. The main properties of the process are derived, such as conditional distribution, autocorrelation structure, innovation structure and jumps. The method of conditional maximum likelihood is used for estimating the process parameters. Some numerical results of the estimators are presented with a brief discussion. In order to illustrate the potential for practice of our process we apply it to a real data set.
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.
A new extended burr XII distribution
(Austrian Society of Statistics, 2017-02) Ghosh, Indranil; Bourguignon, Marcelo
In this paper, we propose a new lifetime distribution, namely the extended Burr XII distribution (using the technique as mentioned in Cordeiro et al. (2015)). We derive some basic properties of the new distribution and provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates of model parameters. For illustrative purposes, two real life data sets have been considered as an application of the proposed model.
A new Pareto-type distribution with applications in reliability and income data
(Physica A, 2016-04) Bourguignon, Marcelo; Saulo, Helton; Fernandez, Rodrigo Nobre
A new Pareto-type distribution is introduced and studied. This new model is a generalization of the well-known Pareto distribution. We derive some of its probabilistic and inferential properties. We deduce the mathematical form of the Lorenz curve and the Gini index associated with the new model. The maximum likelihood estimators are derived and their performance are evaluated through a Monte Carlo simulation study. Finally, we illustrate the flexibility of the new distribution by means of three applications to real data sets.
A new skew integer valued time series process
(Statistical Methodology, 2016-01) Bourguignon, Marcelo; Vasconcellos, Klaus L.P.
In this paper, we introduce a stationary first-order integer-valued autoregressive process with geometric–Poisson marginals. The new process allows negative values for the series. Several properties of the process are established. The unknown parameters of the model are estimated using the Yule–Walker method and the asymptotic properties of the estimator are considered. Some numerical results of the estimators are presented with a brief discussion. Possible application of the process is discussed through a real data example.
On moment-type estimators for a class of log-symmetric distributions
(Computacional Statistics, 2017) Balakrishnan, N.; Saulo, Helton; Bourguignon, Marcelo; Zhu, Xiaojun
In this paper, we propose three simple closed form estimators for a class of log-symmetric distributions on R+. The proposed methods make use of some key properties of this class of distributions.We derive the asymptotic distributions of these estimators. The performance of the proposed estimators are then compared with those of themaximum likelihood estimators through MonteCarlo simulations. Finally, some illustrative examples are presented to illustrate the methods of estimation developed here.
Poisson–geometric INAR(1) process for modeling count time series with overdispersion
(Statistica Neerlandica, 2016) Bourguignon, Marcelo
In this paper, we propose a new first-order non-negative integervalued autoregressive [INAR(1)] process with Poisson–geometric marginals based on binomial thinning for modeling integer-valued time series with overdispersion. Also, the new process has, as a particular case, the Poisson INAR(1) and geometric INAR(1) processes. The main properties of the model are derived, such as probability generating function, moments, conditional distribution, higher-order moments, and jumps. Estimators for the parameters of process are proposed, and their asymptotic properties are established. Some numerical results of the estimators are presented with a discussion of the obtained results. Applications to two real data sets are given to show the potentiality of the new process.
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.
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.
The exponentiated generalized gumbel distribution
(Revista Colombiana de Estadistica, 2015-01) Andrade, Thiago; Rodrigues, Heloisa; Bourguignon, Marcelo; Cordeiro, Gauss
A class of univariate distributions called the exponentiated generalized class was recently proposed in the literature. A four-parameter model within this class named the exponentiated generalized Gumbel distribution is defined. We discuss the shapes of its density function and obtain explicit expressions for the ordinary moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. The density function of the order statistic is derived. The method of maximum likelihood is used to estimate model parameters. We determine the observed information matrix. We provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates of model parameters and two applications to real data to illustrate the importance of the new model.
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 Gomes
We 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.
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.
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.
The transmuted birnbaum-saunders distribuition
(Revstat Statistical Journal, 2017-10) Bourguignon, Marcelo; Leão, Jeremias; Leiva, Víctor; Santos-Neto, Manoel
The Birnbaum–Saunders distribution has been largely studied and applied because of its attractive properties. We introduce a transmuted version of this distribution. Various of its mathematical and statistical features are derived. We use the maximum likelihood method for estimating its parameters and determine the score vector and Hessian matrix for inference and diagnostic purposes. We evaluate the performance of the maximum likelihood estimators by a Monte Carlo study. We illustrate the potential applications of the new transmuted Birnbaum–Saunders distribution by means of three real-world data sets from different areas.

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Navegando por Autor "Bourguignon, Marcelo"