A pathway from Bayesian statistical analysis to superstatistics |
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Authors: | AM Mathai HJ Haubold |
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Institution: | a Centre for Mathematical Sciences, Pala Campus, Arunapuram P.O., Pala, Kerala 686574, India b Department of Mathematics and Statistics, McGill University, Canada H3A2K6 c Office for Outer Space Affairs, United Nations, P.O. Box 500, Vienna International Centre, A-1400 Vienna, Austria |
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Abstract: | Superstatistics and Tsallis statistics in statistical mechanics are given an interpretation in terms of Bayesian statistical analysis. Subsequently superstatistics is extended by replacing each component of the conditional and marginal densities by Mathai’s pathway model and further both components are replaced by Mathai’s pathway models. This produces a wide class of mathematically and statistically interesting functions for prospective applications in statistical physics. It is pointed out that the final integral is a particular case of a general class of integrals introduced by the authors earlier. Those integrals are also connected to Krätzel integrals in applied analysis, inverse Gaussian densities in stochastic processes, reaction rate integrals in the theory of nuclear astrophysics and Tsallis statistics in nonextensive statistical mechanics. The final results are obtained in terms of Fox’s H-function. Matrix variate analogue of one significant specific case is also pointed out. |
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Keywords: | Mathai&rsquo s pathway model Fox H-function Superstatistics Tsallis statistics Bayesian analysis Krä tzel integral Extended beta models |
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