  An approach will be proposed to determine the existence of a limit
distribution of additive arithmetic functions in this work. It is based on
assertions that will be proven in this work and on the properties of Dirichlet
convolution and M\"obius inversion. Based on this approach, formulas will be
obtained for finding the mean and variance for the limit distribution of
additive arithmetic functions. Examples of this approach to proving the
existence of a limit distribution of additive arithmetic functions and finding
the mean value and variance for the limit distribution of additive arithmetic
functions are considered.
