  For numerical semigroups with a specified list of (not necessarily minimal)
generators, we obtain explicit asymptotic expressions, and in some cases
quasipolynomial/quasirational representations, for all major factorization
length statistics. This involves a variety of tools that are not standard in
the subject, such as algebraic combinatorics (Schur polynomials), probability
theory (weak convergence of measures, characteristic functions), and harmonic
analysis (Fourier transforms of distributions). We provide instructive examples
which demonstrate the power and generality of our techniques. We also highlight
unexpected consequences in the theory of homogeneous symmetric functions.
