A Study of Understand the Weighted Maxwell- Boltzmann Distribution

Exploring the Statistical Distribution of Particle Speed in an Idealized Gas

Abstract

The Maxwell Distribution is often used in physics, especially statistical mechanics, to describethe speed of a particle in an idealized gas. James Clerk Maxwell, a Scottish physicist, suggested thisdistribution in 1859. In 1871, a German scientist named Ludwig Boltzmann built on Maxwell's work toexplain how energy is distributed among molecules. The speed of a particle travelling through threedimensionalspace may be seen as a collection of independent and normally distributed random variables,each with a mean and variance equal to one-third of the rate parameter, which is the focus of the majorityof the study.Derivation of weighted Maxwell-Boltzmann distribution, weighted distribution, Maximumlikelihood estimation, Structural properties, Estimation of parameters, Maximum likelihood estimation