arXiv subjects

Filidor Vilca

Publications and source records attributed to Filidor Vilca.

3 recordsLinked to original sources

arXiv2026

Quantile autoregressive moving average models for ratio-based bounded time series

This paper proposes the quantile unit-log-symmetric autoregressive moving average (QULS--ARMA) model for bounded time series on the open unit interval $(0,1)$. The model extends the unit-log-symmetric family by introducing a quantile-based reparameterization and embedding autoregressive and moving-average dynamics directly in the conditional quantile, thereby overcoming limitations of mean-based approaches and providing a coherent framework for proportion data arising from ratios of dependent positive variables. The proposed specification accommodates asymmetric behavior and heavy tails through flexible log-symmetric kernels, including the normal and Student-$t$ distributions. Parameter estimation is carried out via conditional maximum likelihood, and asymptotic properties are established. Monte Carlo simulations and an empirical application to hydroelectric energy storage proportions in Brazil assess the finite-sample performance and practical advantages of the QULS--ARMA model. The results show the good performance of the proposed estimators across a range of scenarios and kernel specifications.

stat.CO↗

arXiv2022

Theoretical results and modeling under the discrete Birnbaum-Saunders distribution

In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability and order statistics are also presented. In addition, we propose a regression model based on the discrete Birnbaum-Saunders distribution. The model parameters are estimated by the maximum likelihood method and a Monte Carlo study is performed to evaluate the performance of the estimators. Finally, we illustrate the proposed methodology with the use of real data sets.

stat.ME↗

arXiv2017

Finite Mixture of Birnbaum-Saunders distributions using the $k$ bumps algorithm

Mixture models have received a great deal of attention in statistics due to the wide range of applications found in recent years. This paper discusses a finite mixture model of Birnbaum- Saunders distributions with G components, as an important supplement of the work developed by Balakrishnan et al. (2011), who only considered two components. Our proposal enables the modeling of proper multimodal scenarios with greater flexibility, where the identifiability of the model with G components is proven and an EM-algorithm for the maximum likelihood (ML) estimation of the mixture parameters is developed, in which the k-bumps algorithm is used as an initialization strategy in the EM algorithm. The performance of the k-bumps algorithm as an initialization tool is evaluated through simulation experiments. Moreover, the empirical information matrix is derived analytically to account for standard error, and bootstrap procedures for testing hypotheses about the number of components in the mixture are implemented. Finally, we perform simulation studies and analyze two real datasets to illustrate the usefulness of the proposed method.

stat.ME↗