Elorrieta, F., Eyheramendy, S., & Palma, W. (2019). Discrete-time autoregressive model for unequally spaced time-series observations. Astron. Astrophys., 627, 11 pp.
Abstract: Most time-series models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There are some techniques that fit unequally spaced time series, such as the continuous-time autoregressive moving average (CARMA) processes. These models are defined as the solution of a stochastic differential equation. It is not uncommon in astronomical time series, that the time gaps between observations are large. Therefore, an alternative suitable approach to modeling astronomical time series with large gaps between observations should be based on the solution of a difference equation of a discrete process. In this work we propose a novel model to fit irregular time series called the complex irregular autoregressive (CIAR) model that is represented directly as a discrete-time process. We show that the model is weakly stationary and that it can be represented as a state-space system, allowing efficient maximum likelihood estimation based on the Kalman recursions. Furthermore, we show via Monte Carlo simulations that the finite sample performance of the parameter estimation is accurate. The proposed methodology is applied to light curves from periodic variable stars, illustrating how the model can be implemented to detect poor adjustment of the harmonic model. This can occur when the period has not been accurately estimated or when the variable stars are multiperiodic. Last, we show how the CIAR model, through its state space representation, allows unobserved measurements to be forecast.
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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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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., 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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Mancini, L., Sarkis, P., Henning, T., Bakos, G. A., Bayliss, D., Bento, J., et al. (2020). The highly inflated giant planet WASP-174b. Astron. Astrophys., 633, 12 pp.
Abstract: Context. The transiting exoplanetary system WASP-174 was reported to be composed by a main-sequence F star (V = 11.8 mag) and a giant planet, WASP-174b (orbital period P-orb = 4.23 days). However only an upper limit was placed on the planet mass (<1.3 M-Jup), and a highly uncertain planetary radius (0.7-1.7 R-Jup) was determined.Aims. We aim to better characterise both the star and the planet and precisely measure their orbital and physical parameters.Methods. In order to constrain the mass of the planet, we obtained new measurements of the radial velocity of the star and joined them with those from the discovery paper. Photometric data from the HATSouth survey and new multi-band, high-quality (precision reached up to 0.37 mmag) photometric follow-up observations of transit events were acquired and analysed for getting accurate photometric parameters. We fit the model to all the observations, including data from the TESS space telescope, in two different modes: incorporating the stellar isochrones into the fit, and using an empirical method to get the stellar parameters. The two modes resulted to be consistent with each other to within 2<sigma>.Results. We confirm the grazing nature of the WASP-174b transits with a confidence level greater than 5 sigma, which is also corroborated by simultaneously observing the transit through four optical bands and noting how the transit depth changes due to the limb-darkening effect. We estimate that approximate to 76% of the disk of the planet actually eclipses the parent star at mid-transit of its transit events. We find that WASP-174b is a highly-inflated hot giant planet with a mass of M-p = 0.330 +/- 0.091 M-Jup and a radius of R-p = 1.435 +/- 0.050 R-Jup, and is therefore a good target for transmission-spectroscopy observations. With a density of rho (p) = 0.135 +/- 0.042 g cm(-3), it is amongst the lowest-density planets ever discovered with precisely measured mass and radius.
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Marchant, C., Leiva, V., Cysneiros, F. J. A., & Vivanco, J. F. (2016). Diagnostics in multivariate generalized Birnbaum-Saunders regression models. J. Appl. Stat., 43(15), 2829–2849.
Abstract: Birnbaum-Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.
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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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Sandford, E., Espinoza, N., Brahm, R., & Jordan, A. (2019). Estimation of singly transiting K2 planet periods with Gaia parallaxes. Mon. Not. Roy. Astron. Soc., 489(3), 3149–3161.
Abstract: When a planet is only observed to transit once, direct measurement of its period is impossible. It is possible, however, to constrain the periods of single transiters, and this is desirable as they are likely to represent the cold and far extremes of the planet population observed by any particular survey. Improving the accuracy with which the period of single transiters can be constrained is therefore critical to enhance the long-period planet yield of surveys. Here, we combine Gaia parallaxes with stellar models and broad-band photometry to estimate the stellar densities of K2 planet host stars, then use that stellar density information to model individual planet transits and infer the posterior period distribution. We show that the densities we infer are reliable by comparing with densities derived through asteroseismology, and apply our method to 27 validation planets of known (directly measured) period, treating each transit as if it were the only one, as well as to 12 true single transiters. When we treat eccentricity as a free parameter, we achieve a fractional period uncertainty over the true single transits of 94(-58)(+87) per cent, and when we fix e = 0, we achieve fractional period uncertainty 15(-6)(+30) per cent, a roughly threefold improvement over typical period uncertainties of previous studies.
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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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