Facultad de Ciencias Básicas

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The Power Muth Distribution*
(Taylor&Francis and VGTU, 2017) Jodrá, Pedro; Gómez, Héctor Wladimir; Jiménez-Gamero, María Dolores; Alba-Fernández, María Virtudes
Muth introduced a probability distribution with application in reliability theory. We propose a new model from the Muth law. This paper studies its statistical properties, such as the computation of the moments, computer generation of pseudo-random data and the behavior of the failure rate function, among others. The estimation of parameters is carried out by the method of maximum likelihood and a Monte Carlo simulation study assesses the performance of this method. The practical usefulness of the new model is illustrated by means of two real data sets, showing that it may provide a better fit than other probability distributions
Modified Slash Lindley Distribution
(Hindawi, 2017) Reyes, Jimmy; Venegas, Osvaldo; Gómez, Héctor W.
Generalized modified slash Birnbaum-Saunders distribution
(MDPI, 2018) Reyes, Jimmy; Barranco-Chamorro, Inmaculada; Gallardo, Diego I.; Gómez, Héctor W.
In this paper, a generalization of the modified slash Birnbaum–Saunders (BS) distribution is introduced. The model is defined by using the stochastic representation of the BS distribution, where the standard normal distribution is replaced by a symmetric distribution proposed by Reyes et al. It is proved that this new distribution is able to model more kurtosis than other extensions of BS previously proposed in the literature. Closed expressions are given for the pdf (probability density functio), along with their moments, skewness and kurtosis coefficients. Inference carried out is based on modified moments method and maximum likelihood (ML). To obtain ML estimates, two approaches are considered: Newton–Raphson and EM-algorithm. Applications reveal that it has potential for doing well in real problems.
Melatonin relations with respiratory Quotient Weaken on acute exposure to high altitude
(Frontiers Media SA, 2018) Tapia, Marcelo; Wulff-Zottele, Cristian; De Gregorio, Nicole; Lang, Moring; Varela, Héctor; Serón-Ferré, María Josefa; Vivaldi, Ennio A; Araneda, Oscar F.; Silva-Urra, Juan; Gunga, Hanss-Christian; Behn, Claus
High altitude (HA) exposure may affect human health and performance by involving the body timing system. Daily variations of melatonin may disrupt by HA exposure, thereby possibly affecting its relations with a metabolic parameter like the respiratory quotient (RQ). Sea level (SL) volunteers (7 women and 7 men, 21.0 ± 2.04 y) were examined for daily changes in salivary melatonin concentration (SMC). Sampling was successively done at SL (Antofagasta, Chile) and, on acute HA exposure, at nearby Caspana (3,270 masl). Saliva was collected in special vials (Salimetrics Oral Swab, United Kingdom) at sunny noon (SMCD) and in the absence of blue light at midnight (SMCN). The samples were obtained after rinsing the mouth with tap water and were analyzed for SMC by immunoassay (ELISA kit; IBL International, Germany). RQ measurements (n = 12) were realized with a portable breath to breath metabolic system (OxiconTM Mobile, Germany), between 8:00 PM and 10:00 PM, once at either location. At SL, SMCD, and SMCN values (mean ± SD) were, respectively, 2.14 ± 1.30 and 11.6 ± 13.9 pg/ml (p < 0.05). Corresponding values at HA were 8.83 ± 12.6 and 13.7 ± 16.7 pg/ml (n.s.). RQ was 0.78 ± 0.07 and 0.89 ± 0.08, respectively, at SL and HA (p < 0.05). Differences between SMCN and SMCD (SMCN–SMCD) strongly correlate with the corresponding RQ values at SL (r = −0.74) and less tight at HA (r = −0.37). Similarly, mean daily SMC values (SMC¯ x) tightly correlate with RQ at SL (r = −0.79) and weaker at HA (r = −0.31). SMCN–SMCD, as well as, SMC¯ x values at SL, on the other hand, respectively, correlate with the corresponding values at HA (r = 0.71 and r = 0.85). Acute exposure to HA appears to loosen relations of SMC with RQ. A personal profile in daily SMC variation, on the other hand, tends to be conserved at HA.
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
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.
The Slashed-Rayleigh Fading Channel Distribution
(Hindawi, 2019) Gomez-Deniz, E.; Gómez, L.; Gómez, H.W.
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.
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
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.
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.
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.
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 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.
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.
Bivariate power-skew-elliptical distribution
(MDPI, 2020) Martínez-Flórez, G.; Tovar-Falón, R.; Gómez, H.W.
In this article, we introduce a power-skew-elliptical (PSE) distribution in the bivariate setting. The new bivariate model arises in the context of conditionally specified distributions. The proposed bivariate model is an absolutely continuous distribution whose marginals are univariate PSEdistributions. The special case of the bivariate power-skew-normal (BPSN) distribution is studied in details. General properties of the BPSN distribution are derived and the estimation of the unknown parameters by maximum pseudo-likelihood is discussed. Further, a sandwich type matrix, which is a consistent estimator for the asymptotic covariance matrix of the maximum likelihood (ML) estimator is determined. Two applications for real data of the proposed bivariate distribution is provided for illustrative purposes.
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.
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
Scale mixture of Rayleigh distribution
(MDPI, 2020) Rivera, P.A.; Barranco-Chamorro, I.; Gallardo, D.I.; Gómez, H.W.
n this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution.
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.

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