Helton Saulo
Universidade Federal de Goiás
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Publication
Featured researches published by Helton Saulo.
Journal of Applied Statistics | 2014
Víctor Leiva; Carolina Marchant; Helton Saulo; Muhammad Aslam; Fernando Rojas
Process capability indices (PCIs) are tools widely used by the industries to determine the quality of their products and the performance of their manufacturing processes. Classic versions of these indices were constructed for processes whose quality characteristics have a normal distribution. In practice, many of these characteristics do not follow this distribution. In such a case, the classic PCIs must be modified to take into account the non-normality. Ignoring the effect of this non-normality can lead to misinterpretation of the process capability and ill-advised business decisions. An asymmetric non-normal model that is receiving considerable attention due to its good properties is the Birnbaum–Saunders (BS) distribution. We propose, develop, implement and apply a methodology based on PCIs for BS processes considering estimation, parametric inference, bootstrap and optimization tools. This methodology is implemented in the statistical software {\tt R}. A simulation study is conducted to evaluate its performance. Real-world case studies with applications for three data sets are carried out to illustrate its potentiality. One of these data sets was already published and is associated with the electronic industry, whereas the other two are unpublished and associated with the food industry.
Stochastic Environmental Research and Risk Assessment | 2013
Helton Saulo; Víctor Leiva; Flávio Augusto Ziegelmann; Carolina Marchant
In this paper, we introduce a new nonparametric kernel method for estimating asymmetric densities based on generalized skew-Birnbaum–Saunders distributions. Kernels based on these distributions have the advantage of providing flexibility in the asymmetry and kurtosis levels. In addition, the generalized skew-Birnbaum–Saunders kernel density estimators are boundary bias free and achieve the optimal rate of convergence for the mean integrated squared error of the nonnegative asymmetric kernel estimators. We carry out a data analysis consisting of two parts. First, we conduct a Monte Carlo simulation study for evaluating the performance of the proposed method. Second, we use this method for estimating the density of three real air pollutant concentration data sets. These numerical results favor the proposed nonparametric estimators.
Computational Statistics & Data Analysis | 2013
Carolina Marchant; Karine Bertin; Víctor Leiva; Helton Saulo
The kernel method is a nonparametric procedure used to estimate densities with support in R. When nonnegative data are modeled, the classical kernel density estimator presents a bias problem in the neighborhood of zero. Several methods have been developed to reduce this bias, which include the boundary kernel, data transformation and reflection methods. An alternative proposal is to use kernel estimators based on distributions with nonnegative support, as is the case of the Birnbaum-Saunders (BS), gamma, inverse Gaussian and lognormal models. Generalized BS (GBS) distributions have received considerable attention, due to their properties and their flexibility in modeling different types of data. In this paper, we propose, characterize and implement the kernel method based on GBS distributions to estimate densities with nonnegative support. In addition, we provide a simple method to choose the corresponding bandwidth. In order to evaluate the performance of these new estimators, we conduct a Monte Carlo simulation study. The obtained results are illustrated by analyzing financial real data.
Computational Statistics & Data Analysis | 2014
Víctor Leiva; Helton Saulo; Jeremias Leão; Carolina Marchant
The Birnbaum-Saunders distribution is receiving considerable attention due to its good properties. One of its extensions is the class of scale-mixture Birnbaum-Saunders (SBS) distributions, which shares its good properties, but it also has further properties. The autoregressive conditional duration models are the primary family used for analyzing high-frequency financial data. We propose a methodology based on SBS autoregressive conditional duration models, which includes in-sample inference, goodness-of-fit and out-of-sample forecast techniques. We carry out a Monte Carlo study to evaluate its performance and assess its practical usefulness with real-world data of financial transactions from the New York stock exchange.
Journal of statistical theory and practice | 2012
Helton Saulo; Jeremias Leão; Marcelo Bourguignon
AbstractMotivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy Birnbaum-Saunders (Kw-
Reliability Engineering & System Safety | 2017
VÃctor Leiva; Fabrizio Ruggeri; Helton Saulo; Juan Vivanco
{\mathcal B}{\mathcal S}
Archive | 2015
Helton Saulo; Víctor Leiva; Fabrizio Ruggeri
ℬS) distribution. This distribution provides an enormous flexibility in modeling heavy-tailed and skewed data. We derive some mathematical properties of the Kw-
Annals of Operations Research | 2013
Helton Saulo; Leandro Chaves Rêgo; Jose Angelo Divino
{\mathcal B}{\mathcal S}
Journal of statistical theory and practice | 2017
N. Balakrishnan; Helton Saulo; Jeremias Leão
ℬS including moments, quantile function, average lifetime function, mean residual lifetime function, and order statistics. In addition, we discuss maximum likelihood estimation of the model parameters.
Environmetrics | 2015
Víctor Leiva; Carolina Marchant; Fabrizio Ruggeri; Helton Saulo
Abstract The Birnbaum–Saunders distribution has been widely studied and applied to reliability studies. This paper proposes a novel use of this distribution to analyze the effect on hardness, a material mechanical property, when incorporating nano-particles inside a polymeric bone cement. A plain variety and two modified types of mesoporous silica nano-particles are considered. In biomaterials, one can study the effect of nano-particles on mechanical response reliability. Experimental data collected by the authors from a micro-indentation test about hardness of a commercially available polymeric bone cement are analyzed. Hardness is modeled with the Birnbaum–Saunders distribution and Bayesian inference is performed to derive a methodology, which allows us to evaluate the effect of using nano-particles at different loadings by the R software.