Departamento de Matemáticas

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http://repositorioabierto.uantof.cl/handle/uantof/222

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Realization of Extremal Spectral Data by Pentadiagonal Matrices
(MDPI, 2024) Pickmann-Soto, Hubert; Arela-Pérez, Susana; Lozano, Charlie; Nina, Hans
In this paper, we address the extremal inverse eigenvalue problem for pentadiagonal matri-ces. We provide sufficient conditions for their existence and realizability through new constructions that consider spectral data of its leading principal submatrices. Finally, we present some examples generated from the algorithmic procedures derived from our results.
New Spectral Results for Laplacian Harary Matrix and the HararyLaplacian-Energy-like Applying a Matrix Order Reduction
(MDPI, 2024) Medina, Luis; Rodríguez, Jonnathan; Trigo, Macarena
In this paper, we introduce the concepts of Harary Laplacian-energy-like for a simple undirected and connected graph Gwith ordern. We also establish novel matrix results in this regard.Furthermore, by employing matrix order reduction techniques, we derive upper and lower bounds utilizing existing graph invariants and vertex connectivity. Finally, we characterize the graphs that achieve the aforementioned bounds by considering the generalized join operation of graphs.
GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations
(MDPI, 2024) Murúa, Nicolás; Coronel, Aníbal; Tello, Alex; Berres, Stefan; Huancas, Fernando
In this paper, we consider the finite difference approximation for a one-dimensional mathematical model of heat conduction in a three-layered solid with interfacial conditions for temperature and heat flux between the layers. The finite difference scheme is unconditionally stable, convergent, and equivalent to the solution of two linear algebraic systems. We evaluate various methods for solving the involved linear systems by analyzing direct and iterative solvers, including GPU-accelerated approaches using CuPy and PyCUDA. We evaluate performance and scalability and contribute to advancing computational techniques for modeling complex physical processes accurately and efficiently.
Semigroup theory and nite element method applied to a non-linear dissipative wave equation
(IOP Publishing Ltd., 2024) Chavez, Gino; Cortes Vega, Luis; Sotomayor, Adrián
We study the wave equation with a non-linear dissipative term associated to a bidimensional membrane with xed boundary. We use the semigroup theory to consider the existence and uniqueness of solutions to the problem and we implement the nite element method to analyse the vibrating evolutionary equation. In particular we use Comsol Multiphysics software with a rectangular mesh to analyze the corresponding evolutionary system. We mention that this system can appear, for example, in the diaphragm of a centrifugal pump in mining processes.
Geogebra in the visualization of integrating factors in non-exact differential equations
(IOP Publishing Ltd., 2024) Olivares, Jorge; Martin, P.; Valero, E.
In the present work, integrating factors used in the solution of non-exact differential equations will be shown with general examples through software application of dynamic geometry GeoGebra. Now these applets are part of theteaching support material in the eigineering careers of the University of Antofagasta on 2020.
Observational cross-sectional study of Trichomonas tenax in patients with periodontal disease attending a Chilean university dental clinic
(BioMed Central, 2019) Bracamonte Wolf, Casandra ; Orrego, Patricio R. ; Muñoz, Christian ; Herrera, Daniel ; Bravo, Joel ; Gonzalez, Jorge ; Varela, Héctor ; Catalán, Alejandro; Araya, Jorge E.
Background: The oral flagellated protozoan Trichomonas tenax has been associated with patients with periodontal disease. However, no recent studies have been conducted on the prevalence of T. tenax in Chile. The aim of this study was to determine the presence of T. tenax in patients with periodontal disease, admitted to the Dental Clinic of the University of Antofagasta, Chile, through Polymerase Chain Reaction (PCR) amplification of the beta-tubulin gene. Methods: An observational, cross-sectional study was conducted on 50 patients diagnosed with periodontal disease, 20 of them with gingivitis and 30 with periodontitis. T. tenax was identified by PCR amplification of the beta-tubulin gene. Associations between the protozoan and periodontal disease or the presence of risk factors to establish T. tenax infection were determined using the chi-square test and binary logistic regression analysis. Results: T. tenax was present in 28 out of 50 (56%) of patients with periodontal disease, and was more prevalent when associated with periodontitis (21 out of 30; 70%) than dental plaque-induced gingivitis (7 out of 20; 35%). Non-statistically-significant associations were observed between the presence of T. tenax and age, gender, smoking habit or diabetes. Statistically significant associations were observed between the presence of T. tenax and periodontal disease, and between T. tenax and the Periodontal Screening and Recording (PSR) index. Conclusion: T. tenax showed a high presence in patients with progressive states of periodontal diseases. Consequently, T. tenax detection is strongly recommended in patients with periodontal disease diagnosis and with a PSR index greater than 3.
Bimodal extension based on the skew-t-normal distribution
(Brazilian Statistical Association, 2019) Amiri, Mehdi; Gómez, Héctor W.; Jamalizadeh, Ahad; Towhidi, Mina
In this paper, a skew and uni-/bi-modal extension of the Student-t distribution is considered. This model is more flexible and has wider ranges of skewness and kurtosis than the other skew distributions in literature. Fisher information matrix for the proposed model and some submodels are derived. With a simulation study and some real data sets, applicability of the proposed models are illustrated.
Univariate and bivariate models related to the generalized epsilon-skew-Cauchy distribution
(MDPI, 2019) Arnold, Barry C.; Gómez, Héctor W.; Varela, Héctor; Vidal, Ignacio
In this paper, we consider a stochastic representation of the epsilon–skew–Cauchy distribution, viewed as a member of the family of skewed distributions discussed in Arellano-Valle et al. (2005). The stochastic representation facilitates derivation of distributional properties of the model. In addition, we introduce symmetric and asymmetric extensions of the Cauchy distribution, together with an extension of the epsilon–skew–Cauchy distribution. Multivariate versions of these distributions can be envisioned. Bivariate examples are discussed in some detail.
Modified Slash Lindley Distribution
(Hindawi, 2017) Reyes, Jimmy; Venegas, Osvaldo; Gómez, Héctor W.
An asymmetric distribution with heavy tails and its expectation-maximization (EM) algorithm implementation
(MDPI, 2019) Olmos, Nevenka M; Venegas, Osvaldo; Gómez, Yolanda M.; Iriarte, Yuri A.
In this paper we introduce a new distribution constructed on the basis of the quotient of two independent random variables whose distributions are the half-normal distribution and a power of the exponential distribution with parameter 2 respectively. The result is a distribution with greater kurtosis than the well known half-normal and slashed half-normal distributions. We studied the general density function of this distribution, with some of its properties, moments, and its coefficients of asymmetry and kurtosis. We developed the expectation–maximization algorithm and present a simulation study. We calculated the moment and maximum likelihood estimators and present three illustrations in real data sets to show the flexibility of the new model.
Modified power-symmetric distribution
(MDPI, 2019) Gómez-Déniz, Emilio; Iriarte, Yuri A.; Calderín-Ojeda, Enrique; Gómez, Héctor W.
In this paper, a general class of modified power-symmetric distributions is introduced. By choosing as symmetric model the normal distribution, the modified power-normal distribution is obtained. For the latter model, some of its more relevant statistical properties are examined. Parameters estimation is carried out by using the method of moments and maximum likelihood estimation. A simulation analysis is accomplished to study the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the modified power-normal distribution with other existing distributions in the literature by using a real dataset.
On properties of the bimodal skew-normal distribution and an application
(MDPI, 2020) Elal-Olivero, David; Olivares-Pacheco, Juan F.; Venegas, Osvaldo; Bolfarine, Heleno; Gómez, Héctor W.
The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.
Skewness of maximum likelihood estimators in the weibull censored data
(MDPI, 2019) Magalhães, Tiago M; Gallardo, Diego I.; Gómez, Héctor W.
In this paper, we obtain a matrix formula of order n−1/2, where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.
An asymmetric bimodal distribution with application to quantile regression
(MDPI, 2019) Gómez, Yolanda M; Gómez-Déniz, Emilio; Venegas, Osvaldo; Gallardo, Diego I.; Gómez, Héctor W.
In this article, we study an extension of the sinh Cauchy model in order to obtain asymmetric bimodality. The behavior of the distribution may be either unimodal or bimodal. We calculate its cumulative distribution function and use it to carry out quantile regression. We calculate the maximum likelihood estimators and carry out a simulation study. Two applications are analyzed based on real data to illustrate the flexibility of the distribution for modeling unimodal and bimodal data
The lambert-F distributions class: An alternative family for positive data analysis
(MDPI, 2020) Iriarte, Yuri A.; De Castro, Mário; Gómez, Héctor W.
In this article, we introduce a new probability distribution generator called the Lambert-F generator. For any continuous baseline distribution F, with positive support, the corresponding Lambert-F version is generated by using the new generator. The result is a new class of distributions with one extra parameter that generalizes the baseline distribution and whose quantile function can be expressed in closed form in terms of the Lambert W function. The hazard rate function of a Lambert-F distribution corresponds to a modification of the baseline hazard rate function, greatly increasing or decreasing the baseline hazard rate for earlier times. Herein, we study the main structural properties of the new class of distributions. Special attention is given to two particular cases that can be understood as two-parameter extensions of the well-known exponential and Rayleigh distributions. Wediscuss parameter estimation for the proposed models considering the moments and maximum likelihood methods. Finally, two applications were developed to illustrate the usefulness of the proposed distributions in the analysis of data from different real settings.
A power maxwell distribution with heavy tails and applications
(MDPI, 2020) Segovia, Francisco A; Gómez, Yolanda M.; Venegas, Osvaldo; Gómez, Héctor W.
In this paper we introduce a distribution which is an extension of the power Maxwell distribution. This new distribution is constructed based on the quotient of two independent random variables, the distributions of which are the power Maxwell distribution and a function of the uniform distribution (0,1) respectively. Thus the result is a distribution with greater kurtosis than the power Maxwell. We study the general density of this distribution, and some properties, moments, asymmetry and kurtosis coefficients. Maximum likelihood and moments estimators are studied. We also develop the expectation–maximization algorithm to make a simulation study and present two applications to real data.
Truncated power-normal distribution with application to non-negative measurements
(MDPI, 2018) Castillo, Nabor O.; Gallardo, Diego I.; Bolfarine, Heleno; Gómez, Héctor W.
This paper focuses on studying a truncated positive version of the power-normal (PN) modelconsidered in Durrans (1992). The truncation point is considered to be zero so that the resulting model is an extension of the half normal distribution. Some probabilistic properties are studied for the proposed model along with maximum likelihood and moments estimation. The model is fitted to two real datasets and compared with alternative models for positive data. Results indicate good performance of the proposed mode
Flexible Birnbaum-Saunders distribution
(MDPI, 2019) Martínez-Flórez, Guillermo; Barranco-Chamorro, Inmaculada; Bolfarine, Heleno; Gómez, HectorW.
In this paper, we propose a bimodal extension of the Birnbaum–Saunders model by including an extra parameter. This new model is termed flexible Birnbaum–Saunders (FBS) and includes the ordinary Birnbaum–Saunders (BS) and the skew Birnbaum–Saunders (SBS) model as special cases. Its properties are studied. Parameter estimation is considered via an iterative maximum likelihood approach. Two real applications, of interest in environmental sciences, are included, which reveal that our proposal can perform better than other competing models.
A bimodal discrete shifted poisson distribution. A case study of tourists' length of stay
(MDPI, 2020) Gómez-Déniz, Emilio; Pérez-Rodríguez, Jorge Vicente; Reyes, Jimmy; Gómez, Héctor W.
Although the Poisson distribution is appropriate for modelling equi-dispersed distributions, it reflects bimodality less well. In this paper, we propose a distribution which is more suitable for the latter purpose. It can be fitted to both positively and negatively skewed data and appears to represent overdispersion phenomena correctly in count data models obtained using a Poisson distribution. Furthermore, the distribution can be normalised in terms of its mean value, and therefore covariates can be included. Our empirical results are based on tourists’ length of stay in the Canary Islands (Spain), a popular holiday destination. The study analyses data supplied by the Canary Islands Tourist Expenditure Survey. Our findings show that the model presented is valid and that the fit obtained is reasonably good.
A Gamma-type distribution with applications
(MDPI, 2020) Iriarte, Yuri A.; Varela, Héctor; Gómez, Héctor J.; Gómez, Héctor W.
This article introduces a new probability distribution capable of modeling positive data that present different levels of asymmetry and high levels of kurtosis. A slashed quasi-gamma random variable is defined as the quotient of independent random variables, a generalized gamma is the numerator, and a power of a standard uniform variable is the denominator. The result is a new three-parameter distribution (scale, shape, and kurtosis) that does not present the identifiability problem presented by the generalized gamma distribution. Maximum likelihood (ML) estimation is implemented for parameter estimation. The results of two real data applications revealed a good performance in real settings.

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