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Castaneda, P., & Reus, L. (2019). Suboptimal investment behavior and welfare costs: A simulation based approach. Financ. Res. Lett., 30, 170–180.
Abstract: We propose a representation of suboptimal investment behavior based on the stochastic discount factor (SDF) paradigm. Suboptimal investment behavior is rationalized as being the investor's optimal decision under a wrong SDF, while wealth trajectories and budget constraints are based on the true SDF. We develop a novel Monte Carlo simulation approach to compute the welfare costs for this suboptimal behavior. We study the suboptimal portfolio choice under CRRA preferences using two financial market models. The Monte Carlo simulation delivers comparable welfare losses to those computed in the original studies, which are based on partial differential equations (PDE) and – finite-difference schemes.
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Fierro, R., & Leiva, V. (2017). A stochastic methodology for risk assessment of a large earthquake when a long time has elapsed. Stoch. Environ. Res. Risk Assess., 31(9), 2327–2336.
Abstract: We propose a stochastic methodology for risk assessment of a large earthquake when a long time has elapsed from the last large seismic event. We state an approximate probability distribution for the occurrence time of the next large earthquake, by knowing that the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is exponential with a rate depending on the asymptotic slope of the cumulative intensity function corresponding to a nonhomogeneous Poisson process. As it is not possible to obtain an empirical cumulative distribution function of the waiting time for the next large earthquake, an estimator of its cumulative distribution function based on existing data is derived. We conduct a simulation study for detecting scenario in which the proposed methodology would perform well. Finally, a real-world data analysis is carried out to illustrate its potential applications, including a homogeneity test for the times between earthquakes.
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Garcia-Papani, F., Uribe-Opazo, M. A., Leiva, V., & Aykroyd, R. G. (2017). Birnbaum-Saunders spatial modelling and diagnostics applied to agricultural engineering data. Stoch. Environ. Res. Risk Assess., 31(1), 105–124.
Abstract: Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum-Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered-which is extremely important for agricultural management.
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Leiva, V., Ferreira, M., Gomes, M. I., & Lillo, C. (2016). Extreme value Birnbaum-Saunders regression models applied to environmental data. Stoch. Environ. Res. Risk Assess., 30(3), 1045–1058.
Abstract: Extreme value models are widely used in different areas. The Birnbaum-Saunders distribution is receiving considerable attention due to its physical arguments and its good properties. We propose a methodology based on extreme value Birnbaum-Saunders regression models, which includes model formulation, estimation, inference and checking. We further conduct a simulation study for evaluating its performance. A statistical analysis with real-world extreme value environmental data using the methodology is provided as illustration.
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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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Leiva, V., Santos-Neto, M., Cysneiros, F. J. A., & Barros, M. (2016). A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution. Appl. Stoch. Models. Bus. Ind., 32(1), 74–89.
Abstract: The Birnbaum-Saunders (BS) distribution is receiving considerable attention. We propose a methodology for inventory logistics that allows demand data with zeros to be modeled by means of a new discrete-continuous mixture distribution, which is constructed by using a probability mass at zero and a continuous component related to the BS distribution. We obtain some properties of the new mixture distribution and conduct a simulation study to evaluate the performance of the estimators of its parameters. The methodology for stochastic inventory models considers also financial indicators. We illustrate the proposed methodology with two real-world demand data sets. It shows its potential, highlighting the convenience of using it by improving the contribution margins of a Chilean food industry. Copyright (c) 2015 John Wiley & Sons, Ltd.
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Leiva, V., Saulo, H., Leao, J., & Marchant, C. (2014). A family of autoregressive conditional duration models applied to financial data. Comput. Stat. Data Anal., 79, 175–191.
Abstract: 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. (C) 2014 Elsevier B.V. All rights reserved.
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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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Marchant, C., Leiva, V., & Cysneiros, F. J. A. (2016). A Multivariate Log-Linear Model for Birnbaum-Saunders Distributions. IEEE Trans. Reliab., 65(2), 816–827.
Abstract: Univariate Birnbaum-Saunders models have been widely applied to fatigue studies. Calculation of fatigue life is of great importance in determining the reliability of materials. We propose and derive new multivariate generalized Birnbaum-Saunders regression models. We use the maximum likelihood method and the EM algorithm to estimate their parameters. We carry out a simulation study to evaluate the performance of the corresponding maximum likelihood estimators. We illustrate the new models with real-world multivariate fatigue data.
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Santos-Neto, M., Cysneiros, F. J. A., Leiva, V., & Barros, M. (2016). Reparameterized Birnbaum-Saunders regression models with varying precision. Electron. J. Stat., 10(2), 2825–2855.
Abstract: We propose a methodology based on a reparameterized Birnbaum-Saunders regression model with varying precision, which generalizes the existing works in the literature on the topic. This methodology includes the estimation of model parameters, hypothesis tests for the precision parameter, a residual analysis and influence diagnostic tools. Simulation studies are conducted to evaluate its performance. We apply it to two real-world case-studies to show its potential with the R software.
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