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In this paper a method of obtaining smooth analytical estimates of probability densities, radial distribution functions and potentials of mean force from sampled data in a statistically controlled fashion is presented. The approach is…
The Holtsmark distribution has applications in plasma physics, for the electric-microfield distribution involved in spectral line shapes for instance, as well as in astrophysics for the distribution of gravitating bodies. It is one of the…
We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
We extend the Kolmogorov--Smirnov (K-S) test to multiple dimensions by suggesting a $\mathbb{R}^n \rightarrow [0,1]$ mapping based on the probability content of the highest probability density region of the reference distribution under…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
In this paper, we describe a method for estimating the joint probability density from data samples by assuming that the underlying distribution can be decomposed as a mixture of product densities with few mixture components. Prior works…
We propose a user-friendly graphical tool, the half-disk density strip (HDDS), for visualizing and comparing probability density functions. The HDDS exploits color shading for representing a distribution in an intuitive way. In univariate…
Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC…
This paper derives the asymptotic distribution of variance weighted Kolmogorov-Smirnov statistics for conditional moment inequality models for the case of a one dimensional covariate. The asymptotic distribution depends on the data…
Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
One aim of data mining is the identification of interesting structures in data. For better analytical results, the basic properties of an empirical distribution, such as skewness and eventual clipping, i.e. hard limits in value ranges, need…
This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a…
This paper develops a geometric reinterpretation of probability in which expectation arises from averaging in probability coordinates rather than in value space. By interpreting the cumulative distribution functions as coordinate maps, a…
How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…
For certain types of statistical models, the characteristic function (Fourier transform) is available in closed form, whereas the probability density function has an intractable form, typically as an infinite sum of probability weighted…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…