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Keywords = skewed-elliptical sinh alpha-power distribution

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18 pages, 445 KiB  
Article
An Exponentiated Skew-Elliptic Nonlinear Extension to the Log–Linear Birnbaum–Saunders Model with Diagnostic and Residual Analysis
by Guillermo Martínez-Flórez, Yolanda M. Gómez and Osvaldo Venegas
Axioms 2023, 12(7), 624; https://doi.org/10.3390/axioms12070624 - 23 Jun 2023
Viewed by 1313
Abstract
In this paper, we propose a nonlinear regression model with exponentiated skew-elliptical errors distributed, which can be fitted to datasets with high levels of asymmetry and kurtosis. Maximum likelihood estimation procedures in finite samples are discussed and the information matrix is deduced. We [...] Read more.
In this paper, we propose a nonlinear regression model with exponentiated skew-elliptical errors distributed, which can be fitted to datasets with high levels of asymmetry and kurtosis. Maximum likelihood estimation procedures in finite samples are discussed and the information matrix is deduced. We carried out a diagnosis of the influence for the nonlinear model. To analyze the sensitivity of the maximum likelihood estimators of the model’s parameters to small perturbations in distribution assumptions and parameter estimation, we studied the perturbation schemes, the case weight, and the explanatory and response variables of perturbations; we also carried out a residual analysis of the deviance components. Simulation studies were performed to assess some properties of the estimators, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a real dataset is presented. Full article
(This article belongs to the Special Issue Probability, Statistics and Estimation)
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16 pages, 993 KiB  
Article
The Skewed-Elliptical Log-Linear Birnbaum–Saunders Alpha-Power Model
by Guillermo Martínez-Flórez, Heleno Bolfarine and Yolanda M. Gómez
Symmetry 2021, 13(7), 1297; https://doi.org/10.3390/sym13071297 - 19 Jul 2021
Cited by 3 | Viewed by 1989
Abstract
In this paper, the skew-elliptical sinh-alpha-power distribution is developed as a natural follow-up to the skew-elliptical log-linear Birnbaum–Saunders alpha-power distribution, previously studied in the literature. Special cases include the ordinary log-linear Birnbaum–Saunders and skewed log-linear Birnbaum–Saunders distributions. As shown, it is able to [...] Read more.
In this paper, the skew-elliptical sinh-alpha-power distribution is developed as a natural follow-up to the skew-elliptical log-linear Birnbaum–Saunders alpha-power distribution, previously studied in the literature. Special cases include the ordinary log-linear Birnbaum–Saunders and skewed log-linear Birnbaum–Saunders distributions. As shown, it is able to surpass the ordinary sinh-normal models when fitting data sets with high (above the expected with the sinh-normal) degrees of asymmetry. Maximum likelihood estimation is developed with the inverse of the observed information matrix used for standard error estimation. Large sample properties of the maximum likelihood estimators such as consistency and asymptotic normality are established. An application is reported for the data set previously analyzed in the literature, where performance of the new distribution is shown when compared with other proposed alternative models. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Distributions: Theoretical Developments and Applications Ⅲ)
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