In statistics we have probability distribution functions which give us likelihood that some random variable ($X$) will equal a particular value. Assuming this variable is continuous, the distribution satisfies: $$ \int f_{X}(x) \ dx = 1 $$
and can be used to obtain the moments of the variable \begin{align} \mu'_i = \int X^i f_x(x) dx \end{align}
In physics we often work with the mass distribution function which describes the distribution of mass. For example the total mass across a system is given by: $$ M_{tot} = \int g_M(m) \ dm $$
and like the statistical PDF we can also derive moments of this mass distribution function by integrating across the distribution function: $$ \mu'_i = \int m g_M(m) \ dm $$
I am wondering what the connection between these two concepts is and if there is any way to move between them?