Leiva, V., Marchant, C., Ruggeri, F., & Saulo, H. (2015). A criterion for environmental assessment using Birnbaum-Saunders attribute control charts. Environmetrics, 26(7), 463–476.
Abstract: Assessing environmental risk is useful for preventing adverse effects on human health in highly polluted cities. We design a criterion for environmental monitoring based on an attribute control chart for the number of dangerous contaminant levels when the concentration to be monitored follows a Birnbaum-Saunders distribution. This distribution is being widely applied to environmental data. We provide a novel justification for its usage in environmental sciences. The control coefficient and the minimum inspection concentration for the designed criterion are determined to yield the specified in-control average run length, whereas the out-of-control case is obtained according to a shift in the target mean. A simulation study is conducted to evaluate the proposed criterion, which reports its performance to provide earlier alerts of out-of-control processes. An application with real-world environmental data is carried out to validate its coherence with what is reported by the health authority. Copyright (c) 2015 John Wiley & Sons, Ltd.
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Lillo, C., Leiva, V., Nicolis, O., & Aykroyd, R. G. (2018). L-moments of the Birnbaum-Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data. J. Appl. Stat., 45(2), 187–209.
Abstract: Understanding patterns in the frequency of extreme natural events, such as earthquakes, is important as it helps in the prediction of their future occurrence and hence provides better civil protection. Distributions describing these events are known to be heavy tailed and positive skew making standard distributions unsuitable for modelling the frequency of such events. The Birnbaum-Saunders distribution and its extreme value version have been widely studied and applied due to their attractive properties. We derive L-moment equations for these distributions and propose novel methods for parameter estimation, goodness-of-fit assessment and model selection. A simulation study is conducted to evaluate the performance of the L-moment estimators, which is compared to that of the maximum likelihood estimators, demonstrating the superiority of the proposed methods. To illustrate these methods in a practical application, a data analysis of real-world earthquake magnitudes, obtained from the global centroid moment tensor catalogue during 1962-2015, is carried out. This application identifies the extreme value Birnbaum-Saunders distribution as a better model than classic extreme value distributions for describing seismic events.
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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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