“…In order to perform a transparent comparison, the framework of MFA is rephrased in its most sophisticated fashion in which the tail part of PDF, giving the probabilities of events larger than its standard deviation, is written down once the multifractal spectrum for the spatial distribution of singularities is specified (see (1) below), whereas the center part, giving the probabilities of events smaller than its standard deviation, is assumed to be analyzed by the Tsallis-type PDF for the variable itself [8,9] (see (2) below). The various PDF's extracted out from the DNS conducted by Gotoh et al [19,20], and the PDF of fluid particle accelerations observed by Bodenschatz et al in their Lagrangian measurement of particle accelerations [21,22,23] will be analyzed with the help of the multifractal spectrums for the log-normal, the p model and the harmonious representation.…”