Departamento de estadisticas y ciencia de datos

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http://repositorioabierto.uantof.cl/handle/uantof/220

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Mostrando 1 - 20 de 48

Unit-Power Half-Normal Distribution Including QuantileRegression with Applications to Medical Data
(2024) Karol I. Santoro; Yolanda M. Gómez; Darlin Soto; Inmaculada Barranco Chamorro
In this paper, we present the unit-power half-normal distribution, derived from the power half-normal distribution, for data analysis in the open unit interval. The statistical properties of the unit-power half-normal model are described in detail. Simulation studies are carried out to evaluate the performance of the parameter estimators. Additionally, we implement the quantile regression for this model, which is applied to two real healthcare data sets. Our findings suggest that the unitpower half-normal distribution provides a robust and flexible alternative for existing models for proportion data
Reparameterized Scale Mixture of Rayleigh DistributionRegression Models with Varying Precision
(2024) Pilar A. Rivera; Diego I. Gallardo; Osvaldo Venegas; Emilio Gómez Déniz; Héctor W. Gómez
In this paper, we introduce a new parameterization for the scale mixture of the Rayleigh distribution, which uses a mean linear regression model indexed by mean and precision parameters to model asymmetric positive real data. To test the goodness of fit, we introduce two residuals for the new model. A Monte Carlo simulation study is performed to evaluate the parameter estimation of the proposed model. We compare our proposed model with existing alternatives and illustrate its advantages and usefulness using Gilgais data in R software version 4.2.3 with the gamlss package
A New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data
(2024) Jimmy Reyes; Mario A. Rojas; Pedro L. Cortés; Jaime Arrué
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 Bimodal Extension of the Beta-Binomial Distributionwith Applications
(2024) Jimmy Reyes; Josu Najera Zuloaga; Dae-Jin Lee; Jaime Arrué; Yuri A. Iriarte
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 Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data
(2024) Neveka M. Olmos; Emilio Gómez-Déniz; Osvaldo Venegas; Héctor W. Gómez
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.
Scale Mixture of Gleser Distribution with an Application toInsurance Data
(2024) Neveka M. Olmos; Emilio Gómez Déniz; Osvaldo Venegas
In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta(a, 1)distribution. The SMG distribution is an alternative to distributions with two parameters and a heavy right tail. We study its representation and some basic properties, maximum likelihood inference, and Fisher ’s information matrix. We present an application to a real dataset in which the SMG distribution shows a better fit than two other known distributions
New Flexible Asymmetric Log-Birnbaum–Saunders Nonlinear Regression Model with Diagnostic Analysis
(2024) Guillermo Martínez Flórez; Inmaculada Barranco Chamorro; Héctor W. Gómez
A nonlinear log-Birnbaum–Saunders regression model with additive errors is introduced. It is assumed that the error term follows a flexible sinh-normal distribution, and therefore it can be used to describe a variety of asymmetric, unimodal, and bimodal situations. This is a novelty since there are few papers dealing with nonlinear models with asymmetric errors and, even more, there are few able to fit a bimodal behavior. Influence diagnostics and martingale-type residuals are proposed to assess the effect of minor perturbations on the parameter estimates, check the fitted model, and detect possible outliers. A simulation study for the Michaelis–Menten model is carried out, covering a wide range of situations for the parameters. Two real applications are included, where the use of influence diagnostics and residual analysis is illustrated.
A Bivariate Power Lindley Survival Distribution
(2024) Guillermo Martínez Flórez; Barry C. Arnold; Héctor W. Gómez
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 Modified Cure Rate Model Based on a Piecewise Distribution with Application to Lobular Carcinoma Data
(2024) Yolanda M. Gómez; John L. Santibañez; Vinicius F. Calsavara; Héctor W. Gómez; Diego I. Gallardo
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.
An Extension of the Akash Distribution: Properties, Inference and Application
(2024) Yolanda M. Gómez; Luis Firinguetti Limone; Diego I. Gallardo; Héctor W. Gómez
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
(2024) Yolanda M. Gómez; Inmaculada Barranco Chamorro; Jaime S. Castillo; Héctor W. Gómez
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.
A New Generalization of the Truncated Gumbel Distributionwith Quantile Regression and Applications
(2024) Héctor J. Gómez; Karol I. Santoro; Diego Ayma; Isaac E. Cortés; Isaac E. Cortés; Tiago M. Magalhães
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 Weighted Skew-Logistic Distribution with Applicationsto Environmental Data
(2024) Isaac Cortés; Jimmy Reyes; Yuri A. Iriarte
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.
Scale Mixture of Exponential Distribution with an Application
(2024) Jorge A. Barahona; Yolanda M. Gómez; Emilio Gómez Déniz; Osvaldo Venegas; Héctor W. Gómez
This article presents an extended distribution that builds upon the exponential distribution.This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers increased flexibility in terms of the kurtosis coefficient. We explore the general density, properties, moments, asymmetry, and kurtosis coefficients of this distribution. Statistical inference is performed using both the moments and maximum likelihood methods. To show the performance of this new model, it is applied to a real dataset with atypical observations. The results indicate that the new model outperforms two other extensions of the exponential distribution.
Modified Unit-Half-Normal Distribution with Applications
(2024) Paulina I. Alvarez; Héctor Varela; Isaac E. Cortés; Osvaldo Venegas; Héctor W. Gómez
In this article, we introduce a new continuous distribution based on the unit interval. Thisdistribution is generated from a transformation of a random variable with half-normal distribution.We study its basic properties, percentiles, moments and order statistics. Maximum likelihoodestimation is applied, and we present a simulation study to observe the behavior of the maximumlikelihood estimators. We examine two applications to real proportions datasets, where the newdistribution is shown to provide a better fit than other distributions defined in the unit interval.
Mathematical Formalization and Applications to Data with Excess of Zeros and Ones of the Unit-Proportional Hazard Inflated Models
(2024) Guillermo Martínez Flórez; Roger Tovar Falón; Héctor W. Gómez
In this study, we model the rate or proportion of a specific phenomenon using a set of known covariates. To fit the regression model, which explains the phenomenon within the intervals (0,1), [0,1), (0,1], or [0,1], we employ a logit link function. This approach ensures that the model’s predictions remain within the appropriate range of zero to one. In cases of inflation at zero, one, or both, the logit link function is similarly applied to model the dichotomous Bernoulli-type variable with a multinomial response. The findings demonstrate that the model yields a non-singular information matrix, ensuring valid statistical inference. This ensures the invertibility of the information matrix, allowing for hypothesis testing based on likelihood statistics regarding the parameters in the model. This is not possible with other asymmetric models, such as those derived from the skew-normal distribution, which has a singular information matrix at the boundary of the skewness parameter. Finally, empirical results show the model’s effectiveness in analyzing proportion data with inflation at zero and one, proving its robustness and practicality for analyzing bounded data in various fields of research
A transmuted version of the generalized half-normal distribution
(2019) Salinas, H.S.; Iriarte, Y.A.; Astorga, J.M.
Bivariate power-skew-elliptical distribution
(2020) Martínez-Flórez, G.; Tovar-Falón, R.; Gómez, H.W.
Bimodal extension based on the skew-t-normal distribution
(2019) Amiri, M.; Gómez, H.W.; Jamalizadeh, A.; Towhidi, M.
Corrigendum to: Skew-normal alpha-power model (Statistics, (2014), 48, 6, (1414-1428), 10.1080/02331888.2013.826659)
(2018) Salinas, H.S.; Gómez, H.W.; Martínez-Flórez, G.; Bolfarine, H.

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