Accurate model for the primordial black hole mass distribution from a peak in the power spectrum

We examine the shape of primordial black hole mass distribution arising from a peak in power spectrum. In light improvements to modeling, we revisit claim that effects critical collapse produce is not described by commonly assumed lognormal, showing this conclusion remains valid, particularly for narrow peaks where insensitive properties and determines minimum width. propose some alternative models may better describe shape, both case much broader effect significant. highlight skew-lognormal generalized model motivated physics as best these possible alternatives. These can be used an accurate fast approximation numerically calculated distribution, allowing efficient implementation MCMC analysis. advocate use one two instead lognormal with sufficiently data, such future LIGO--Virgo observations, or when considering strongly dependent constraints on PBH abundance.