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Student'st- andr-distributions: Unified derivation from an entropic variational principle

Authors
Journal
Physica A Statistical Mechanics and its Applications
0378-4371
Publisher
Elsevier
Publication Date
Volume
236
Identifiers
DOI: 10.1016/s0378-4371(96)00395-0
Keywords
  • Generalized Entropy
  • Viriational Principle
  • Student'St-Distribution
  • R-Distribution

Abstract

Abstract The optimization of the recently generalized entropy of the form S q ≡ 1 − ∝ dx[ p( x)] q ∼/( q−1) with the constraints ∝ dx p( x) = 1 and 〈 x 2〉 q ≡ ∝ dx x 2[ p( x)] q = 1 yields the Student's t-distribution for q > 1, and the r-distribution for q < 1.

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