Facultad de Ciencias Básicas

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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 Bimodal Extension of the Beta-Binomial Distributionwith Applications
(MDPI, 2024) Reyes, Jimmy; Najera Zuloaga, Josu; Lee, Dae-Jin; Arrué, Jaime; Iriarte, Yuri A.
In this paper, we propose an alternative distribution to model count data exhibitinguni/bimodality. It arises as a weighted version of the beta-binomial distribution, which is defined bya parametric weight function that admits up to two modes for the resulting probability mass function.Like the baseline beta-binomial distribution, the proposed distribution performs well in modelingoverdispersed binomial data. Structural properties of the new distribution are studied. Raw momentsare derived, which are used to describe the dispersion behavior relative to the mean and the skewnessbehavior. Parameter estimation is carried out using the maximum likelihood method. A simulationstudy is conducted in order to illustrate the behavior of the estimators. Finally, two applicationsillustrating the usefulness of the proposal are presented.
A Bivariate Power Lindley Survival Distribution
(MDPI, 2024) Martínez-Flórez, Guillermo; Arnold, Barry C.; Gómez, Héctor W.
We introduce and investigate the properties of new families of univariate and bivariate distributions based on the survival function of the Lindley distribution. The univariate distribution,to reflect the nature of its construction, is called a power Lindley survival distribution. The basic distributional properties of this model are described. Maximum likelihood estimates of the parameters of the distribution are studied and the corresponding information matrix is identified. A bivariate power Lindley survival distribution is introduced using the technique of conditional specification.The corresponding joint density and marginal and conditional densities are derived. The product moments of the distribution are obtained, together with bounds on the range of correlations that can be exhibited by the model. Estimation of the parameters of the model is implemented by maximizing the corresponding pseudo-likelihood function. The asymptotic variance–covariance matrix of these estimates is investigated. A simulation study is performed to illustrate the performance of these parameter estimates. Finally some examples of model fitting using real-world data sets are described
A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data
(MDPI AG, 2024) Olmos, Neveka M.; Gómez-Déniz, Emilio; Venegas, Osvaldo; Gómez, Héctor W.
The half-normal distribution is composited with the Pareto model to obtain a uni-parametric distribution with a heavy right tail, called the composite half-normal-Pareto distribution. This new distribution is useful for modeling positive data with atypical observations. We study the properties and the behavior of the right tail of this new distribution. We estimate the parameter using a method based on percentiles and the maximum likelihood method and assess the performance of the maximum likelihood estimator using Monte Carlo. We report three applications, one with simulated data and the others with income and expenditure data, in which the new distribution presents better performance than the Pareto distribution.
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.
A Modified Cure Rate Model Based on a Piecewise Distribution with Application to Lobular Carcinoma Data
(MDPI, 2024) Gómez, Yolanda M.; Santibañez, John L.; Calsavara, Vinicius F.; Gómez, Héctor W.; Gallardo, Diego I.r.author
A novel cure rate model is introduced by considering, for the number of concurrent causes, the modified power series distribution and, for the time to event, the recently proposed power piecewise exponential distribution. This model includes a wide variety of cure rate models, such as binomial, Poisson, negative binomial, Haight, Borel, logarithmic, and restricted generalized Poisson. Some characteristics of the model are examined, and the estimation of parameters is performed using the Expectation–Maximization algorithm. A simulation study is presented to evaluate the performance of the estimators in finite samples. Finally, an application in a real medical dataset from a population-based study of incident cases of lobular carcinoma diagnosed in the state of São Paulo, Brazil, illustrates the advantages of the proposed model compared to other common cure rate models in the literature, particularly regarding the underestimation of the cure rate in other proposals and the improved precision in estimating the cure rate of our proposal.
A New Generalization of the Truncated Gumbel Distributionwith Quantile Regression and Applications
(MDPI, 2024) Gómez, Héctor J.; Santoro, Karol I.; Ayma, Diego; Cortés, Isaac E.; Magalhães, Tiago M.
In this article, we introduce a new model with positive support. This model is an extension of the truncated Gumbel distribution, where a shape parameter is incorporated that provides greater flexibility to the new model. The model is parameterized in terms of the p-thquantile of the distribution to perform quantile regression in this model. An extensive simulation study demonstrates the good performance of the maximum likelihood estimators in finite samples. Finally, two applications to real datasets related to the level of beta-carotene and body mass index are presented.
A New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data
(MDPI, 2024) Reyes, Jimmy; Rojas, Mario A.; Cortés, Pedro L.; Arrué, Jaime
The skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have studied extensions based on the skew distribution to model this type of data. In this article, a new family is introduced,consisting of a multimodal modification to the family of skew distributions. Using the methodology of the weighted version of a function, we perform the product of the density function of a family of skew distributions with a polynomial of degree 4, thus obtaining a more flexible model that allows modeling data sets, whose distribution contains at most three modes. The density function, some properties, moments, skewness coefficients, and kurtosis of this new family are presented. This study focuses on the particular cases of skew-normal and Laplace distributions, although it can be applied to any other distribution. A simulation study was carried out, to study the behavior of the model parameter estimates. Illustrations with real data, referring to medicine and environmental data, show the practical performance of the proposed model in the two particular cases presented.
A parametric quantile regression model for asymmetric response variables on the real line
(MDPI, 2020) Gallardo, D.I.; Bourguignon, M.; Galarza, C.E.; Gómez, H.W.
In this paper, we introduce a novel parametric quantile regression model for asymmetric response variables, where the response variable follows a power skew-normal distribution. By considering a new convenient parametrization, these distribution results are very useful for modeling different quantiles of a response variable on the real line. The maximum likelihood method is employed to estimate the model parameters. Besides, we present a local influence study under different perturbation settings. Some numerical results of the estimators in finite samples are illustrated. In order to illustrate the potential for practice of our model, we apply it to a real dataset
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.
A reliability model based on the incomplete generalized integro-exponential function
(MDPI, 2020) Astorga, J.M.; Reyes, J.; Santoro, K.I.; Venegas, O.; Gómez, H.W.
This article introduces an extension of the Power Muth (PM) distribution for modeling positive data sets with a high coefficient of kurtosis. The resulting distribution has greater kurtosis than the PM distribution. We show that the density can be represented based on the incomplete generalized integro-exponential function. We study some of its properties and moments, and its coefficients of asymmetry and kurtosis. We apply estimations using the moments and maximum likelihood methods and present a simulation study to illustrate parameter recovery. The results of application to two real data sets indicate that the new model performs very well in the presence of outliers.
A Weighted Skew-Logistic Distribution with Applicationsto Environmental Data
(MDPI, 2024) Cortés, Isaac; Reyes, Jimmy; Iriarte, Yuri A.
Skewness and bimodality properties are frequently observed when analyzing environmental data such as wind speeds, precipitation levels, and ambient temperatures. As an alternative to modeling data exhibiting these properties, we propose a flexible extension of the skew-logistic distribution. The proposal corresponds to a weighted version of the skewed logistic distribution, defined by a parametric weight function that allows shapes with up to three modes for the resulting density.Parameter estimation via the maximum likelihood approach is discussed. Simulation experiments are carried out to evaluate the performance of the estimators. Applications to environmental data illustrating the utility of the proposal are presented.
Accurate Analytical Approximation for the Bessel Function J2(x)
(MDPI, 2024) Martin, Pablo; Ramos Andrade, Juan Pablo; Caro Pérez, Fabián; Lastra, Freddy
We obtain an accurate analytic approximation for the Bessel function 𝐽2(𝑥) using an improved multipoint quasirational approximation technique (MPQA). This new approximation is valid for all real values of the variable x, with a maximum absolute error of approximately 0.009. These errors have been analyzed in the interval from 𝑥=0 to 𝑥=1000, and we have found that the absolute errors for large x decrease logarithmically. The values of x at which the zeros of the exact function 𝐽2(𝑥) and the approximated function 𝐽˜2(𝑥) occur are also provided, exhibiting very small relative errors. The largest relative error is for the second zero, with 𝜀rel=0.0004 , and the relative errors continuously decrease, reaching 0.0001 for the eleventh zero. The procedure to obtain this analytic approximation involves constructing a bridge function that connects the power series with the asymptotic approximation. This is achieved by using rational functions combined with other elementary functions, such as trigonometric and fractional power functions.
Alkali-Activated Mine Tailings and Solid Wastes as Precursors for Geopolymers
(Avestia, 2024) Samarina, Tatiana; Reyes, Arturo; Letelier, María Victoria; Castillo Godoy, Daniza; Silva Urrego, Yimmy; Cuevas, Jacqueline; Takaluoma, Esther
Former mining activities may pose a threat to the environment if not being handled correctly due to neglecting proper conservation methods at the time of mine closure. While dumping is the most common way of disposing of solid industrial waste such as tailings, fly and bottom ashes, slags etc., those materials are in fact a valuable source of secondary raw minerals. Thus, they could be recycled in a variety of products to turn the waste streams into value via the promising geopolymerisation technology. This article presents a study on the conversion of mine tailings and industrial by-products into geopolymers. Geopolymers based on alumino-silicate fines (steel-making slags and mine tailings) were synthesized using alkaline activation comprising sodium silicate. While the hardening of compositions occurs slowly at ambient temperature, elevated temperatures could change the leaching behaviour and decrease copper release from geopolymer matrix. Compressive strength of the proposed composition was 49±2 MPa after 90 days of curing. The results provide insights of possible reduction of the environmental footprints and potential economic benefits of mine tailings-based geopolymer composites for building applications utilizing mine tailings as suitable concrete material.
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
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.
An Extension of the Akash Distribution: Properties, Inference and Application
(MDPI, 2024) Gómez, Yolanda M.; Firinguetti Limone, Luis; Gallardo, Diego I.; Gómez, Héctor W.
In this article we introduce an extension of the Akash distribution. We use the slash methodology to make the kurtosis of the Akash distribution more flexible. We study the general probability density function of this new model, some properties, moments, skewness and kurtosis coefficients. Statistical inference is performed using the methods of moments and maximum likelihood via the EM algorithm. A simulation study is carried out to observe the behavior of the maximum likelihood estimator. An application to a real data set with high kurtosis is considered, where it is shown that the new distribution fits better than other extensions of the Akash distribution.
An Extension of the Fréchet Distribution and Applications
(MDPI, 2024) Gómez, Yolanda M.; Barranco Chamorro, Inmaculada; Castillo, Jaime S.; Gómez, Héctor W.
This paper presents the Slash-Exponential-Fréchet distribution, which is an expanded version of the Fréchet distribution. Through its stochastic representation, probability distribution function, moments and other relevant features are obtained. Evidence supports that the updated model displays a lighter right tail than the Fréchet model and is more flexible as for skewness and kurtosis. Results on maximum likelihood estimators are given. Our proposition’s applicability is demonstrated through a simulation study and the evaluation of two real-world datasets.
Aqueous Dried Extract of Skytanthus acutus Meyen as Corrosion Inhibitor of Carbon Steel in Neutral Chloride Solutions
(MDPI, 2021) Cáceres, Luis; Frez, Yohana; Galleguillos, Felipe; Soliz, Alvaro; Gómez-Silva, Benito; Borquez, Jorge
The implementation of corrosion engineering control methods and techniques is crucial to extend the life of urban and industrial infrastructure assets and industrial equipment affected by natural corrosion. Then, the search of stable and environmentally friendly corrosion inhibitors is an important pending task. Here, we provide experimental evidence on the corrosion inhibitory activity of aqueous extracts of Skytanthus acutus Meyen leaf, a native plant from the Atacama Desert in northern Chile. Skytanthus extracts as a powder should be prepared at 55 °C to avoid thermal decomposition and loss of corrosion inhibitory activity. Corrosion of carbon steel AISI1020 immersed in 0.5 M NaCl was evaluated in the presence of different doses of Skytanthus extract by complementary and simultaneous linear polarization, electrochemical impedance spectroscopy, and weight-loss technique under high hydrodynamic conditions. Mixed Potential Theory was applied to confirm the electrochemical activity of the extract inhibitory capabilities. The Skytanthus extracts reached a 90% corrosion inhibitory efficiency when tested at 100 to 1200 ppm in a time span of 48 h, through an electrochemical interaction between the extract inhibitor component and the carbon steel surface. The corrosion inhibition activity observed in Skytanthus dry extracts involves a protective film formation by a mechanism that includes an iron dissolution at the expense of either oxygen reduction and/or hydrogen evolution, followed by a ferrous-ferric iron cycling, the formation of an iron complex and adsorption to the metal surface, and, finally, desorption or degradation of the protecting film. The water-soluble plant extract was subjected to HPLC-MS analyses that rendered 14 major signals, with quinic acid, protocatechuic acid, chlorogenic acid isomers, vanillic acid hexoside, and patuletin 3-methoxy-7-glucoside as the most abundant components. Then, we propose that a phenolic derivative is responsible for the corrosion inhibitory activity found in Skytanthus extracts.
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.

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