Related papers: Stochastic comparisons, differential entropy and v…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the…
This paper investigates probability density functions (PDFs) that are continuous everywhere, nearly uniform around the mode of distribution, and adaptable to a variety of distribution shapes ranging from bell-shaped to rectangular. From the…
Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…
In this paper, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advantages of…
We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few…
In a recent letter, Christian Beck described a theoretical link between a family of stochastic differential equations and the probability density functions (PDF) derived from the formalism of nonextensive statistical mechanics. He applied…
With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
A new sharp inequality featuring the differential R\'enyi entropy, the R\'enyi divergence and the R\'enyi cross-entropy of a pair of probability density functions is established. The equality is reached when one of the probability density…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…
The probability distribution function (PDF) of the mass surface density of molecular clouds provides essential information about the structure of molecular cloud gas and condensed structures out of which stars may form. In general, the PDF…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…