Studentʹs t- and r-distributions: Unified derivation from an entropic variational principle

The optimization of the recently generalized entropy of the form Sq ≡ 1 − ∝dx[p(x)]q /(q−1) with the constraints ∝dx p(x) = 1 and x2 q ≡ ∝dx x2[p(x)]q = 1 yields the Studentʹs t-distribution for q> 1, and the r-distribution for q < 1.