Distribution function

This article describes the distribution function as used in physics. You may be looking for the related mathematical concepts of probability density function or cumulative distribution function.

In molecular kinetic theory in physics, a particle's distribution function is a function of seven variables, $f (x, y, z, t; v x, v y, v z)$ , which gives the number of particles per unit volume in phase space. It is the number of particles having approximately the velocity $(v x, v y, v z)$ near the place $(x, y, z)$ and time $(t)$ . The usual normalization of the distribution function is

$n(x,y,z,t) = \int f \,dv_x \,dv_y \,dv_z$

$N(t) = \int n \,dx \,dy \,dz$