Likelihood Based Inference and Bias Reduction in the Modified Skew-t-Normal Distribution
Likelihood Based Inference and Bias Reduction in the Modified Skew-t-Normal Distribution
Authors
Arrue, Jaime
Arellano-Valle, Reinaldo B.
Calderin-Ojeda, Enrique
Venegas, Osvaldo
Gomez, Hector W.
Arellano-Valle, Reinaldo B.
Calderin-Ojeda, Enrique
Venegas, Osvaldo
Gomez, Hector W.
Profesor GuĆa
Authors
Date
Datos de publicaciĆ³n:
10.3390/math11153287
MATHEMATICS,Vol.11,2023
MATHEMATICS,Vol.11,2023
Tipo de recurso
Article
Keywords
Materia geogrƔfica
Collections
Abstract
In this paper, likelihood-based inference and bias correction based on Firth's approach are developed in the modified skew-t-normal (MStN) distribution. The latter model exhibits a greater flexibility than the modified skew-normal (MSN) distribution since it is able to model heavily skewed data and thick tails. In addition, the tails are controlled by the shape parameter and the degrees of freedom. We provide the density of this new distribution and present some of its more important properties including a general expression for the moments. The Fisher's information matrix together with the observed matrix associated with the log-likelihood are also given. Furthermore, the non-singularity of the Fisher's information matrix for the MStN model is demonstrated when the shape parameter is zero. As the MStN model presents an inferential problem in the shape parameter, Firth's method for bias reduction was applied for the scalar case and for the location and scale case.