scholarly journals Flexible Birnbaum–Saunders Distribution

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1305 ◽  
Author(s):  
Guillermo Martínez-Flórez ◽  
Inmaculada Barranco-Chamorro ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Environmental Sciences ◽  
Maximum Likelihood Approach ◽  
Special Cases ◽  
Competing Models ◽  
Likelihood Approach ◽  
Iterative Maximum Likelihood ◽  
Extra Parameter ◽  
Better Than

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.

scholarly journals THE BIVARIATE EXTENSION OF AMOROSO DISTRIBUTION

2020 ◽  
Vol 4 (2) ◽  
pp. 261-283
Author(s):  
David Sam Jayakumar ◽  
A Sulthan ◽  
W Samuel
Keyword(s):  
Maximum Likelihood ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Characteristic Functions ◽  
Estimation Of Parameters ◽  
Numerical Application ◽  
Hazard Functions ◽  
Maximum Likelihood Approach ◽  
Special Cases ◽  
Likelihood Approach

This paper introduces the bivariate extension of the amoroso distribution and its density function is expressed in terms of hyper-geometric function. The standard amoroso distribution, cumulative distribution functions, conditional distributions, and its moments are also derived. The Product moments, Co-variance, correlations, and Shannon’s differential entropy are also shown. Moreover, the generating functions such as moment, Cumulant, Characteristic functions are expressed in Fox-wright function, and the Survival, hazard, and Cumulative hazard functions are also computed. The special cases of the bivariate amoroso distribution are also discussed and nearly 780 bivariate mixtures of distributions can be derived. Finally, the two-dimensional probability surfaces are visualized for the selected special cases and we also showed the estimation of parameters by the method of maximum likelihood approach, and the constrained maximum likelihood approach is also computed by using Non-linear Programming with a numerical application

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