On generalized distributions and pathways

The scalar version of the pathway model of Mathai [A.M. Mathai, Linear Alg. Appl. 396 (2005) 317] is shown to be associated with a large number of probability models used in physics. Different families of densities are listed here, which are all connected through the pathway parameter α, generating...

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Bibliographic Details
Published in:Physics letters. A 2008, Vol.372 (12), p.2109-2113
Main Authors: Mathai, A.M., Haubold, H.J.
Format: Article
Language:English
Subjects:
Generalized entropy measures
Pathway model
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Summary:The scalar version of the pathway model of Mathai [A.M. Mathai, Linear Alg. Appl. 396 (2005) 317] is shown to be associated with a large number of probability models used in physics. Different families of densities are listed here, which are all connected through the pathway parameter α, generating a distributional pathway. The idea is to switch from one functional form to another through this parameter and it is shown that one can proceed from the generalized type-1 beta family to generalized type-2 beta family to generalized gamma family. It is also shown that the pathway model is available by maximizing a generalized measure of entropy, leading to an entropic pathway, covering the particularly interesting cases of Tsallis statistics [C. Tsallis, J. Stat. Phys. 52 (1988) 479] and superstatistics [C. Beck, E.G.D. Cohen, Physica A 322 (2003) 267].
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2007.10.084