Multivariate and matrix-variate analogues of Maxwell–Boltzmann and Raleigh densities

2020

Mathematics

A real scalar variable integral is known in the literature by different names in different disciplines. It is basically a Bessel integral called specifically Krätzel integral. An integral transform with this Krätzel function as kernel is known as Krätzel transform. This article examines some mathematical properties of Krätzel integral, its connection to Mellin convolutions and statistical distributions, its computable representations, and its extensions to multivariate and matrix-variate cases, in both the real and complex domains. An extension in the pathway family of functions is also explored.

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“…Its support is finite or it is a finite-range density, whereas in Equation 24it is of infinite range and x > 0 there. When α → 1, both Equations (24) and (25) go to the model…”

Section: Pathway Extension Of Krätzel Integralmentioning

confidence: 99%

Section: Pathway Extension Of Krätzel Integralmentioning

confidence: 99%

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Mathematical Aspects of Krätzel Integral and Krätzel Transform

2020

Mathematics

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“…Then for α < 1 one has type-1 beta case in (25), for α > 1 one has the type-2 beta case in (26) and for α → 1 one has the gamma case in (27).…”

Section: Raleigh Density and Optimization Of The Generalized Entropymentioning

confidence: 99%

“…Note that the energy density is the case for γ = 1, p = 1. Recently, [26] constructed matrix-variate analogues of the Maxwell-Boltzmann and Raleigh densities.…”

mentioning

confidence: 99%

A generalized entropy optimization and Maxwell–Boltzmann distribution

2018

Eur. Phys. J. B

Abstract. Based on the results of the diffusion entropy analysis of Super-Kamiokande solar neutrino data, a generalized entropy, introduced earlier by the first author is optimized under various conditions and it is shown that Maxwell-Boltzmann distribution, Raleigh distribution and other distributions can be obtained through such optimization procedures. Some properties of the entropy measure are examined and then Maxwell-Boltzmann and Raleigh densities are extended to multivariate cases. Connections to geometrical probability problems, isotropic random points, and spherically symmetric and elliptically contoured statistical distributions are pointed out.

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Erdélyi-Kober Fractional Integrals in the Real Matrix-Variante Case

SpringerBriefs in Mathematical Physics

2018