We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the ...

We propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for such estimators. We suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quad...

various statistical methods have been proposed in terms of predicting the outcomes of facing special factors. in the classical approaches,  making the probability distribution or known probability density functions is ordinarily necessary to predict the desired outcome. however, most of the times enough information about the probability distribution of studied variables is not available to the ...