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Khosravi, M., Leiva, V., Jamalizadeh, A., & Porcu, E. (2016). On a nonlinear Birnbaum-Saunders model based on a bivariate construction and its characteristics. Commun. Stat.-Theory Methods, 45(3), 772–793.
Abstract: The Birnbaum-Saunders (BS) distribution is an asymmetric probability model that is receiving considerable attention. In this article, we propose a methodology based on a new class of BS models generated from the Student-t distribution. We obtain a recurrence relationship for a BS distribution based on a nonlinear skew-t distribution. Model parameters estimators are obtained by means of the maximum likelihood method, which are evaluated by Monte Carlo simulations. We illustrate the obtained results by analyzing two real data sets. These data analyses allow the adequacy of the proposed model to be shown and discussed by applying model selection tools.
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Leiva, V., Ruggeri, F., Saulo, H., & Vivanco, J. F. (2017). A methodology based on the Birnbaum-Saunders distribution for reliability analysis applied to nano-materials. Reliab. Eng. Syst. Saf., 157, 192–201.
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. (C) 2016 Elsevier Ltd. All rights reserved.
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Sanchez, L., Leiva, V., Caro-Lopera, F. J., & Cysneiros, F. J. A. (2015). On matrix-variate Birnbaum-Saunders distributions and their estimation and application. Braz. J. Probab. Stat., 29(4), 790–812.
Abstract: Diverse phenomena from the real-world can be modeled using random matrices, allowing matrix-variate distributions to be considered. The normal distribution is often employed in this modeling, but usually the mentioned random matrices do not follow such a distribution. An asymmetric non-normal model that is receiving considerable attention due to its good properties is the Birnbaum-Saunders (BS) distribution. We propose a statistical methodology based on matrix-variate BS distributions. This methodology is implemented in the statistical software R. A simulation study is conducted to evaluate its performance. Finally, an application with real-world matrix-variate data is carried out to illustrate its potentiality and suitability.
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Santos-Neto, M., Cysneiros, F. J. A., Leiva, V., & Barros, M. (2014). A Reparameterized Birnbaum-Saunders Distribution And Its Moments, Estimation And Applications. REVSTAT-Stat. J., 12(3), 247–272.
Abstract: The Birnbaum-Saunders (BS) distribution is a model that is receiving considerable attention due to its good properties. We provide some results on moments of a reparameterized version of the BS distribution and a generation method of random numbers from this distribution. In addition, we propose estimation and inference for the mentioned parameterization based on maximum likelihood, moment, modified moment and generalized moment methods. By means of a Monte Carlo simulation study, we evaluate the performance of the proposed estimators. We discuss applications of the reparameterized BS distribution from different scientific fields and analyze two real-world data sets to illustrate our results. The simulated and real data are analyzed by using the R software.
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Wanke, P., Ewbank, H., Leiva, V., & Rojas, F. (2016). Inventory management for new products with triangularly distributed demand and lead-time. Comput. Oper. Res., 69, 97–108.
Abstract: This paper proposes a computational methodology to deal with the inventory management of new products by using the triangular distribution for both demand per unit time and lead-time. The distribution for demand during lead-time (or lead-time demand) corresponds to the sum of demands per unit time, which is difficult to obtain. We consider the triangular distribution because it is useful when a distribution is unknown due to data unavailability or problems to collect them. We provide an approach to estimate the probability density function of the unknown lead-time demand distribution and use it to establish the suitable inventory model for new products by optimizing the associated costs. We evaluate the performance of the proposed methodology with simulated and real-world demand data. This methodology may be a decision support tool for managers dealing with the measurement of demand uncertainty in new products. (C) 2015 Elsevier Ltd. All rights reserved.
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