An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences
Abstract
:1. Introduction
Gaussian or normal density for | |
Maxwell-Boltzmann density | |
Rayleigh density | |
Hermert density | |
U-shaped density | |
Student-t for ν degrees of freedom, | |
Caushy density for | |
Standard type-1 beta density | |
Standard type-2 beta density | |
Tsallis statistics in Astrophysics, Power law, q-binomial density | |
Triangular density | |
F-density | |
Helley’s density in physics | |
Gamma density | |
Chisquare density for ν degrees of freedom | |
Exponential density (Laplace density with ) | |
Generalized gamma density | |
Weibull density | |
Logistic density for | |
Fermi-Dirac density, |
1.1. Pathway Model from Mathai’s Entropy Measure
- (i)
- (i)
- (i)
- (i)
1.2. Laplacian Density and Stochastic Processes
1.3. Mittag-Leffler Density and Processes
1.4. Laplace Transform of the Pathway Model
1.5. Multivariate Generalizations
2. Connections to Astrophysics and Statistical Mechanics
2.1. Superstatistics Consideration and Pathway Model
2.2. α-gamma Models Associated with Bessel Function
2.3. Tsallis Statistics
2.4. Extension of Thermonuclear Functions through Pathway Model
2.4.1. Inverse Gaussian as a Particular Case of the Pathway Model
2.4.2. An Interpretation of the Pathway Parameter α
3. Pathway Model and Fractional Calculus
3.1. -Transform
4. A Matrix Variate Pathway Model
4.1. The Normalizing Constants
4.2. Density of the Volume Content
4.3. Connection to Likelihood Ratio Criteria
4.4. Quadratic Forms
4.5. Pathway Fractional Integral
5. Open Problem
Acknowledgments
Conflicts of Interest
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Sebastian, N.; S. Nair, S.; P. Joseph, D. An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences. Axioms 2015, 4, 530-553. https://doi.org/10.3390/axioms4040530
Sebastian N, S. Nair S, P. Joseph D. An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences. Axioms. 2015; 4(4):530-553. https://doi.org/10.3390/axioms4040530
Chicago/Turabian StyleSebastian, Nicy, Seema S. Nair, and Dhannya P. Joseph. 2015. "An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences" Axioms 4, no. 4: 530-553. https://doi.org/10.3390/axioms4040530