Limit distribution of Hodge spectral exponents of irreducible plane curve singularities

We study the distribution of the Hodge spectral exponents of an irreducible plane curve by comparing it with a continuous distribution. We provide a closed formula for this difference in terms of numerical invariants of the curve. We characterize those families of irreducible plane curves whose limit distribution of Hodge spectral exponents is the continuous distribution and we provide intervals of dominating values.