(a) The bilateral exponential is defined by $${ \frac{1}{2}\alpha e^{-\alpha|x|} }$$. Here, $${ \alpha }$$ is the scale parameter. This distribution has an expected value of $${ 0 }$$ and a variance ...

Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, “Probability is the most important concept in modern science, especially as nobody has the ...

A Matlab toolbox for solving the generalized density evolution equation (GDEE) in the probability density evolution method (PDEM) by finite difference method.

Abstract: Non-linear filters consider probability density functions in various non-parametric representations. They often suffer from the curse of dimensionality. Computation of weights over a grid of ...

A long-standing challenge in statistical mechanics has been to quantify the nonequilibrium nature of active systems such as swarming bacteria, schooling fish, and flocking birds. The entropy ...

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 ...

Abstract: An analytical derivation of the EMG signal’s amplitude probability density function (EMG PDF) is presented and used to study how an EMG signal builds-up, or fills, as the degree of muscle ...

Complex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the ...