Jaynes-Gibbs Entropic Convex Duals and Orthogonal Polynomials.

ABSTRACT: The univariate noncentral distributions can be derived by multiplying their central distributions with translation factors. When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become generating functions for classical families of orthogonal polynomials. The ultraspherical noncentral t, normal N, F, and χ2 distributions are thus found to be associated with the Gegenbauer, Hermite, Jacobi, and Laguerre polynomial families, respectively, with the corresponding central distributions standing for the polynomial family-defining weights. Obtained through an unconstrained minimization of the Gibbs potential, Jaynes' maximal entropy priors are formally expressed in terms of the empirical densities' entropic convex

SUBMITTER: Le Blanc R 

PROVIDER: S-EPMC9141810 | biostudies-literature | 2022 May

REPOSITORIES: biostudies-literature