Expected allele frequency distribution of SNVs in real NGS data
I don't have enough experience to answer which probabilistic distribution should be used.

However, this questions also also asks how to estimate parameters of the distributions. If a binomial distribution is chosen, then Heng Li's paper titled "A statistical framework for SNP calling, mutation discovery, association mapping and population genetical parameter estimation from sequencing data" 1 is probably the definitive one. Section 2.3.1 of that paper describes an EM algorithm for estimating allele frequencies from multiple samples under the assumption of Hardy-Weinberg equilibrium for arbitrary but constant ploidy.