Related papers: Efficient Evaluation of the Probability Density Fu…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a…
We show a statistical version of Taylor's theorem and apply this result to non-parametric density estimation from truncated samples, which is a classical challenge in Statistics \cite{woodroofe1985estimating, stute1993almost}. The…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
This paper shows how sparse, high-dimensional probability distributions could be represented by neurons with exponential compression. The representation is a novel application of compressive sensing to sparse probability distributions…
Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
We obtain a formula for the density of the free convolution of an arbitrary probability measure on the unit circle of $\mathbb{C}$ with the free multiplicative analogues of the normal distribution on the unit circle. This description relies…
We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…
In this paper, we study the Dvoretzky covering problem with non-uniformly distributed centers. When the probability law of the centers admits an absolutely continuous density which satisfies a regular condition on the set of essential…
In many applications, the curvature of the space supporting the data makes the statistical modelling challenging. In this paper we discuss the construction and use of probability distributions wrapped around manifolds using exponential…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…