Harmonious Representation of PDF's reflecting Large Deviations

Abstract

The framework of multifractal analysis (MFA) is distilled to the most sophisticated one. Within this transparent framework, it is shown that the harmonious representation of MFA utilizing two distinct Tsallis distribution functions, one for the tail part of probability density function (PDF) and the other for its center part, explains the recently observed PDF's of turbulence in the highest accuracy superior to the analyses based on other models such as the log-normal model and the $p$ model.