Abstract: Quaternion random signals can be analyzed using augmented second-order statistics. If these signals are treated as the augmented quaternion valued random variables, then they can be modeled ...

The integration of distributed generation (DG) into modern electric grids has garnered considerable interest due to its potential to enhance energy resiliency, reduce carbon emissions, and improve ...

Abstract: Random feature latent variable models (RFLVMs) are state-of-the-art tools for uncovering structure in high-dimensional, non-Gaussian data. However, their reliance on Monte Carlo sampling ...

where \(dX(t) = -U'\big (X (t), k \big )\, dt\) describes a deterministic dynamical system evolving in a potential U, dN stands for external noise, X(t) is a realization of the system at time t, and k ...

Probability is the backbone of data science and machine learning, providing essential tools to model uncertainty and variability. This article explores the foundational concepts: random variables, ...

ABSTRACT: In this paper, we explore the dynamic relationship between exchange rates, natural gas, and crude oil prices using the wavelet vine copula approach. The vine copula method offers the ...

The mathematician Daniel Litt has driven social media users to distraction with a series of simple-seeming but counterintuitive probability puzzles. In late January, Daniel Litt posed an innocent ...

A probability distribution is a list of all of the possible outcomes of a random variable along with their corresponding probability values. It helps us understand how that data is spread out. Simply ...

What Is A Probability Density Function? A probability density function, also known as a bell curve, is a fundamental statistics concept, that describes the likelihood of a continuous random variable ...

All the scripts were developed on MATLAB 2023a (compatible with MATLAB 2022b or later). This file contains two main scripts: CoherentBasis.m FockBasis.m which define two types of classes. The first ...

Quantum annealing (QA) can be competitive to classical algorithms in optimizing continuous-variable functions when running on appropriate hardware, show researchers from Tokyo Tech. By comparing the ...

We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual ...