Velocity distribution ($f(\mathbf{v})$)

A function specifying how a particle population is distributed over velocities. If $f$ is a number-density distribution, $f(\mathbf{v})d^{3}v$ counts particles per unit spatial volume in that velocity element and $\int f{d}^{3}v=n$. A probability-density convention instead has integral one. The normalization must be stated before adding populations or comparing their slopes.