  The mutual derivation between arbitrary distribution forms of momenta and
momentum components of particles produced in an isotropic emission source are
systematically studied in terms of probability theory and mathematical
statistics. The distributions of rapidities and pseudorapidities are
expediently studied. As an example, the classical and relativistic ideal gas
models are used to show these distributions by the analytic and Monte Carlo
methods. As an application, the experimental rapidity and transverse momentum
spectra of light flavor particles produced in high energy collisions are
analyzed by a multi-component relativistic ideal gas model in which the single
model can be replaced by other models and distributions.
