Limiting Approach to Generalized Gamma Bessel Model via Fractional Calculus and its Applications in Various Disciplines

2013/07/30 by Nicy Sebastian, Sebastian, Nicy
Mathematics · Physics and Astronomy · #Data Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistics Theory (math.ST) #Statistics and Probability (physics.data-an) #math-ph #math.MP #math.ST #physics.data-an #stat.TH

paper · pdf · doi:10.48550/arxiv.1307.7949

arXiv admin note: text overlap with arXiv:0705.0148 by other authors

arxiv created 2013/07/30 · arxiv updated 2013/07/31

Abstract

The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one can list out almost all the extended densities for the pathway parameter q < 1 and q → 1. Here we bring out the idea of thicker or thinner tailed models associated with a gamma type distribution as a limiting case of pathway operator. Applications of this extended gamma model in Statistical Mechanics, input-output models, and solar spectral irradiance modeling etc are established.

Citations

• Superstatistics, thermodynamics, and fluctuations

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