Related papers: Mills' ratio: Reciprocal convexity and functional …
Large transverse momentum distributions of identified particles observed at RHIC are analyzed by a relativistic stochastic model in the three dimensional (non-Euclidean) rapidity space. A distribution function obtained from the model is…
This paper continues a series of studies devoted to analysis of the bivariate probability distribution P(x,y) of two consecutive price increments x (push) and y (response) at intraday timescales for a group of stocks. Besides the asymmetry…
We discuss conditions under which a convex cone $\K\subset \R^{\Omega}$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely…
Subaddivity type matrix inequalities for concave funcions and symetric norms are given.
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
A rigorous connection between large deviations theory and Gamma-convergence is established. Applications include representations formulas for rate functions, a contraction principle for measurable maps, a large deviations principle for…
Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of…
Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this letter, a stochastic univariate model and the associated probability distribution function…
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…
We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $\infty-$Wasserstein…
The particle distribution function that describes two interpenetrating plasma streams is re-investigated. It is shown how, based on the Maxwell-Boltzmann-J\"uttner distribution function that has been derived almost a century ago, a…
A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal…
Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the…
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…
We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula…
Probability distribution theory helps in studying the impact of various dimensions in life while the Mittag-Leffler function and bicomplex are used in electromagnetism, quantum mechanics, and signal theory. Considering the importance of…
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…
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…
Let K be a random variable following a truncated exponential distribution. Such distributions are described by a single parameter here denoted by $\gamma$. The determination of $\gamma$ by Maximum Likelihood methods leads to a…