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A Type I Generalized Logistic Distribution: Solving Its Estimation Problems with a Bayesian Approach and Numerical Applications Based on Simulated and Engineering Data. Symmetry (Basel) 2022. [DOI: 10.3390/sym14040655] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
The family of logistic type distributions has been widely studied and applied in the literature. However, certain estimation problems exist in some members of this family. Particularly, the three-parameter type I generalized logistic distribution presents these problems, where the parameter space must be restricted for the existence of their maximum likelihood estimators. In this paper, motivated by the complexities that arise in the inference under the likelihood approach utilizing this distribution, we propose a Bayesian approach to solve these problems. A simulation study is carried out to assess the performance of some posterior distributional characteristics, such as the mean, using Monte Carlo Markov chain methods. To illustrate the potentiality of the Bayesian estimation in the three-parameter type I generalized logistic distribution, we apply the proposed method to real-world data related to the copper metallurgical engineering area.
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2
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Saulo H, Souza R, Vila R, Leiva V, Aykroyd RG. Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum-Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data. SENSORS 2021; 21:s21196518. [PMID: 34640834 PMCID: PMC8512640 DOI: 10.3390/s21196518] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Revised: 09/22/2021] [Accepted: 09/25/2021] [Indexed: 12/18/2022]
Abstract
Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum–Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum–Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.
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Affiliation(s)
- Helton Saulo
- Department of Statistics, Universidade de Brasília, Brasília 70910-90, Brazil; (H.S.); (R.S.); (R.V.)
| | - Rubens Souza
- Department of Statistics, Universidade de Brasília, Brasília 70910-90, Brazil; (H.S.); (R.S.); (R.V.)
| | - Roberto Vila
- Department of Statistics, Universidade de Brasília, Brasília 70910-90, Brazil; (H.S.); (R.S.); (R.V.)
| | - Víctor Leiva
- School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile
- Correspondence: or
| | - Robert G. Aykroyd
- Department of Statistics, University of Leeds, Leeds, West Yorkshire LS2 9JT, UK;
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Modeling the Risk of Infectious Diseases Transmitted by Aedes aegypti Using Survival and Aging Statistical Analysis with a Case Study in Colombia. MATHEMATICS 2021. [DOI: 10.3390/math9131488] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Many infectious diseases are deadly to humans. The Aedes aegypi mosquito is the principal vector of infectious diseases that include chikungunya, dengue, yellow fever, and zika. Some factors such as survival time and aging are vital in its development and capacity to transmit the pathogens, which in turn are affected by environmental factors such as temperature. In this paper, we consider aging as the biological wear and tear presented in some mosquito populations over time, whereas survival is considered as the maximum time that a mosquito lives. We propose statistical methods that are commonly used in engineering for reliability analysis to compare transmission riskiness among different mosquitoes. We conducted a case study in three Colombian cities: Bello, Riohacha, and Villavicencio. In this study, we detected that the Aedes aegypi female mosquitoes in Bello live longer than in Riohacha and Villavicencio, and the females in Riohacha live longer than those in Villavicencio. Regarding aging, the females from Riohacha age slower than in Villavicencio and the latter age slower than in Bello. Mosquito populations that age slower are considered young and the other ones are old. In addition, we detected that the females from Bello in the temperature range of 27 ∘C–28 ∘C age slower than those in Bello at higher temperatures. In general, a young female has a higher risk of transmitting a disease to humans than an old female, regardless of its survival time. These findings have not been previously reported in studies of this type of infectious diseases and contributed to new knowledge in biomedicine.
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Saulo H, Dasilva A, Leiva V, Sánchez L, la Fuente‐Mella H. Log‐symmetric quantile regression models. STAT NEERL 2021. [DOI: 10.1111/stan.12243] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Helton Saulo
- Department of Statistics Universidade de Brasília Brasília Brazil
| | - Alan Dasilva
- Department of Statistics Universidade de Brasília Brasília Brazil
| | - Víctor Leiva
- School of Industrial Engineering Pontificia Universidad Católica de Valparaíso Valparaíso Chile
| | - Luis Sánchez
- Institute of Statistics Universidad Austral de Chile Valdivia Chile
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Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model. MATHEMATICS 2021. [DOI: 10.3390/math9060645] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Improving air quality is an important environmental challenge of our time. Chile currently has one of the most stable and emerging economies in Latin America, where human impact on natural resources and air quality does not go unperceived. Santiago, the capital of Chile, is one of the cities in which particulate matter (PM) levels exceed national and international limits. Its location and climate cause critical conditions for human health when interaction with anthropogenic emissions is present. In this paper, we propose a predictive model based on bivariate regression to estimate PM levels, related to PM2.5 and PM10, simultaneously. Birnbaum-Saunders distributions are used in the joint modeling of real-world PM2.5 and PM10 data by considering as covariates some relevant meteorological variables employed in similar studies. The Mahalanobis distance is utilized to assess bivariate outliers and to detect suitability of the distributional assumption. In addition, we use the local influence technique for analyzing the impact of a perturbation on the overall estimation of model parameters. In the predictions, we check the categorization for the observed and predicted cases of the model according to the primary air quality regulations for PM.
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Chekkal S, Lagha K, Zougab N. Generalized Birnbaum–Saunders kernel for hazard rate function estimation. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1887228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Sylia Chekkal
- Laboratory LMA, University of Bejaia, Bejaia, Algeria
| | - Karima Lagha
- Laboratory LaMOS, University of Bejaia, Bejaia, Algeria
| | - Nabil Zougab
- Laboratory LaMOS, University of Bejaia, Bejaia, Algeria
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Dasilva A, Dias R, Leiva V, Marchant C, Saulo H. [Invited tutorial] Birnbaum–Saunders regression models: a comparative evaluation of three approaches. J STAT COMPUT SIM 2020. [DOI: 10.1080/00949655.2020.1782912] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Affiliation(s)
- Alan Dasilva
- Department of Statistics, Universidade de Brasília, Brasília, Brazil
| | - Renata Dias
- Department of Statistics, Universidade de Brasília, Brasília, Brazil
| | - Victor Leiva
- School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
| | - Carolina Marchant
- Faculty of Basic Sciences, Universidad Católica del Maule, Talca, Chile
| | - Helton Saulo
- Department of Statistics, Universidade de Brasília, Brasília, Brazil
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Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers. MATHEMATICS 2020. [DOI: 10.3390/math8081259] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Both cell-wise and case-wise outliers may appear in a real data set at the same time. Few methods have been developed in order to deal with both types of outliers when formulating a regression model. In this work, a robust estimator is proposed based on a three-step method named 3S-regression, which uses the comedian as a highly robust scatter estimate. An intensive simulation study is conducted in order to evaluate the performance of the proposed comedian 3S-regression estimator in the presence of cell-wise and case-wise outliers. In addition, a comparison of this estimator with recently developed robust methods is carried out. The proposed method is also extended to the model with continuous and dummy covariates. Finally, a real data set is analyzed for illustration in order to show potential applications.
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Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data. MATHEMATICS 2020. [DOI: 10.3390/math8061000] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
In the present paper, a novel spatial quantile regression model based on the Birnbaum–Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum–Saunders distribution, where one of its parameters is associated with the quantile of the respective marginal distribution, is established. The model parameters are estimated by the maximum likelihood method. Finally, a data set is applied for illustrating the formulated model.
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Cavieres MF, Leiva V, Marchant C, Rojas F. A Methodology for Data-Driven Decision-Making in the Monitoring of Particulate Matter Environmental Contamination in Santiago of Chile. REVIEWS OF ENVIRONMENTAL CONTAMINATION AND TOXICOLOGY 2020; 250:45-67. [PMID: 32318823 DOI: 10.1007/398_2020_41] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Atmospheric pollution derives mainly from anthropogenic activities that use combustion and may lead to adverse effects in exposed populations. It is generally accepted that air contamination causes cardiovascular and pulmonary morbidity in addition to increased mortality after exposure, but other epidemiological associations have also been described, including cancer as well as reproductive and immunological toxicity. Thus the concentration of chemicals in the air must be controlled. We propose that monitoring of air quality may be achieved by employing data analytics to generate information within the context of data-driven decision making to prevent and/or adequately alert the population about possible critical episodes of air contamination. In this paper, we propose a methodology for monitoring particulate matter pollution in Santiago of Chile which is based on bivariate control charts with heavy-tailed asymmetric distributions. This methodology is useful for monitoring environmental risk when the particulate matter concentrations follow bivariate Birnbaum-Saunders or Birnbaum-Saunders-t-Student distributions. A case study with real particulate matter pollution from Santiago is provided, which shows that the methodology is suitable to alert early episodes of extreme air pollution. The results are in agreement with the critical episodes reported with the current model used by the Chilean health authority.
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Affiliation(s)
| | - Víctor Leiva
- School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
| | - Carolina Marchant
- Faculty of Basic Sciences, Universidad Católica del Maule, Talca, Chile
| | - Fernando Rojas
- Faculty of Pharmacy, Universidad de Valparaíso, Valparaíso, Chile
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Arrué J, Arellano-Valle RB, Gómez HW, Leiva V. On a new type of Birnbaum-Saunders models and its inference and application to fatigue data. J Appl Stat 2019; 47:2690-2710. [DOI: 10.1080/02664763.2019.1668365] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Jaime Arrué
- Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile
| | | | - Héctor W. Gómez
- Department of Mathematics, Universidad de Antofagasta, Antofagasta, Chile
| | - Víctor Leiva
- School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
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Negarestani H, Jamalizadeh A, Shafiei S, Balakrishnan N. Mean mixtures of normal distributions: properties, inference and application. METRIKA 2018. [DOI: 10.1007/s00184-018-0692-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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