Related papers: Density and Distribution Evaluation for Convolutio…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The…
The sum of correlated gamma random variables appears in the analysis of many wireless communications systems, e.g. in systems under Nakagami-m fading. In this Letter we obtain exact expressions for the probability density function (PDF) and…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative.…
It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a non stationary diffusion equation. Implications of this result for kernel density estimation of the condensed…
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…
The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process…
In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…
Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…
An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…
Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…
We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
Free probability and random matrix theory has shown to be a fruitful combination in many fields of research, such as digital communications, nuclear physics and mathematical finance. The link between free probability and eigenvalue…
A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the…
A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos…