arXiv subjects

Víctor Leiva

Publications and source records attributed to Víctor Leiva.

3 recordsLinked to original sources

arXiv2020

Log-symmetric quantile regression models

Regression models based on the log-symmetric family of distributions are particularly useful when the response is strictly positive and asymmetric. In this paper, we propose a class of quantile regression models based on reparameterized log-symmetric distributions, which have a quantile parameter. Two Monte Carlo simulation studies are carried out using the R software. The first one analyzes the performance of the maximum likelihood estimators, the information criteria AIC, BIC and AICc, and the generalized Cox-Snell and random quantile residuals. The second one evaluates the performance of the size and power of the Wald, likelihood ratio, score and gradient tests. A real box office data set is finally analyzed to illustrate the proposed approach.

stat.ME↗

arXiv2018

A new mixture-based fixed-effect model for a biometrical case-study related to immunogenecity with highly censored data

We propose a new continuous-discrete mixture regression model which is useful for describing highly censored data. We motivate our investigation based on a case-study in biometry related to measles vaccines in Haiti. In this case-study, the neutralization antibody level is explained by the type of vaccine used, level of the dosage and gender of the patient. This mixture model allows us to account for excess of censored observations and consists of the Birnbaum-Saunders and Bernoulli distributions. These distributions describe the antibody level and the point mass of the censoring observations. We estimate the model parameters with the maximum likelihood method. Numerical evaluation of the model is performed by Monte Carlo simulations and by an illustration with biometrical data, both of which show its good performance and its potential applications.

stat.ME↗

arXiv2016

A model for risk assessment of a large earthquake with application to Chilean data

We study the asymptotic distribution for the occurrence time of the next large earthquake, by knowing the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is asymptotically exponential with a rate depending on the asymptotic slope of the cumulative intensity function corresponding to a non-homogeneous Poisson process. Moreover, as it is not possible to obtain an empirical cumulative distribution function for the waiting time of the next large earthquake, a random cumulative function based on existing data is stated. We demonstrate that analogous results to the theorems of Glivenko-Cantelli and Kolmogorov are satisfied by this random cumulative function. We conduct a simulation study for detecting in what scenario the approximate distribution of the studied elapsed time performs well. Finally, a real-world data analysis is carried out to illustrate the potential applications of our proposal.

math.ST↗