Maximum likelihood estimation for scale-shape mixtures of flexible generalized skew normal distributions via selection representation

2021 ◽  
Author(s):  
Abbas Mahdavi ◽  
Vahid Amirzadeh ◽  
Ahad Jamalizadeh ◽  
Tsung-I Lin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Normal Distributions ◽  
Skew Normal Distributions ◽  
Skew Normal

scholarly journals On Properties of the Bimodal Skew-Normal Distribution and an Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 703
Author(s):  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco ◽  
Osvaldo Venegas ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Normal Distributions ◽  
Stochastic Representations ◽  
Skew Normal

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.

scholarly journals The Extended Birnbaum–Saunders Distribution Based on the Scale Shape Mixture of Skew Normal Distributions

2021 ◽  
Vol 20 (4) ◽  
pp. 481-517
Author(s):  
Tahereh Poursadeghfard ◽  
Alireza Nematollahi ◽  
Ahad Jamalizadeh
Keyword(s):  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Parameter Estimates ◽  
Asymptotic Covariance Matrix ◽  
Finite Sample ◽  
Data Set ◽  
Normal Distributions ◽  
Skew Normal Distributions ◽  
Skew Normal

AbstractIn this article, a large class of univriate Birnbaum–Saunders distributions based on the scale shape mixture of skew normal distributions is introduced which generates suitable subclasses for modeling asymmetric data in a variety of settings. The moments and maximum likelihood estimation procedures are disscused via an ECM-algorithm. The observed information matrix to approximate the asymptotic covariance matrix of the parameter estimates is then derived in some subclasses. A simulation study is also performed to evaluate the finite sample properties of ML estimators and finally, a real data set is analyzed for illustrative purposes.

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