An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences

  • Sebastian N
  • S. Nair S
  • P. Joseph D
N/ACitations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter , called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized type-2 beta family of densities, and generalized gamma family of densities, in the scalar as well as the matrix cases, also in the real and complex domains. It is shown that when the model is applied to physical situations then the current hot topics of Tsallis statistics and superstatistics in statistical mechanics become special cases of the pathway model, and the model is capable of capturing many stable situations as well as the unstable or chaotic neighborhoods of the stable situations and transitional stages. The pathway model is shown to be connected to generalized information measures or entropies, power law, likelihood ratio criterion or -criterion in multivariate statistical analysis, generalized Dirichlet densities, fractional calculus, Mittag-Leffler stochastic process, Krätzel integral in applied analysis, and many other topics in different disciplines. The pathway model enables one to extend the current results on quadratic and bilinear forms, when the samples come from Gaussian populations, to wider classes of populations. 36pt

Cite

CITATION STYLE

APA

Sebastian, N., S. Nair, S., & P. Joseph, D. (2015). An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences. Axioms, 4(4), 530–553. https://doi.org/10.3390/axioms4040530

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free