Maximum entropy pdfs and the moment problem under near-Gaussian conditions

This paper focuses on a class of continuous probability density functions (pdfs) that are generated by the maximum entropy method (mem), which are of potential interest in fluid dynamics. It discusses their properties and presents a method for obtaining approximate solutions to the moment problem that is associated with this class of pdfs. The method allows one to express pdf parameters in terms of constrained moments, alone. The results thus obtained hold for pdfs that represent small perturbations from a known pdf within this class. On combining these results with exact moment equations, one obtains successful approximations to the closure relations that are associated with these pdfs. The Gaussian pdf belongs in this class, and the method can be used to explore the near-Gaussian region.