Related papers: Stochastic comparisons, differential entropy and v…
A probabilistic description is essential for understanding growth processes far from equilibrium. In this paper, we compute time-dependent Probability Density Functions (PDFs) in order to investigate stochastic logistic and Gompertz models,…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
We show that the parton distribution functions (PDF) described by the statistical model have very interesting physical properties which help to understand the structure of partons. The role of the quark helicity components is emphasized as…
We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the…
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
The surge in digitized text data requires reliable inferential methods on observed textual patterns. This article proposes a novel two-sample text test for comparing similarity between two groups of documents. The hypothesis is whether the…
We connect shift-invariant characteristic kernels to infinitely divisible distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two…
Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these…
Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the…
We present the first prediction of the probability distribution function (PDF) for self-organization of shear flows modeled by a nonlinear diffusion equation with a stochastic forcing. A novel non-perturbative method based on a coherent…
We derive a multifractal model for the velocity probability density distribution function (PDF), which is valid from the inertial range to the viscous range. The model gives a continuous evolution of velocity PDFs from large to small…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
We focus on the probability distribution function (pdf) $P(\Delta \gamma; \gamma)$ where $\Delta \gamma$ are the {\em measured} strain intervals between plastic events in an athermal strained amorphous solids, and $\gamma$ measures the…
Transfer Entropy and Directed Information are information-theoretic measures of the directional dependency between stochastic processes. Following the definitions of Schreiber and Massey in discrete time, we define and evaluate these…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…