Table 2.

Empirical and model Tanimoto score distribution parameters

Distribution	μ	σ	ρ
Tanimoto (ChemDB)	0.17	0.052	0.82
Tanimoto (fT(t)ChemDB)	0.16	0.055	0.82
Tanimoto (Binomial)	0.12	0.017	0.28
Tanimoto (Multiple Bernoulli)	0.18	0.018	0.25
Tanimoto (Hypergeometric/Gaussian)	0.10	0.050	0.90

The parameters were determined from Gaussian fits to the distributions, except for the ratio-of-Gaussians parameters (f_T(t)_ChemDB), which were determined directly from the analytical formula for f_T(t). The intersection and union correlations are also given. The ratio-of-Gaussians approximation gives accurate estimates of the empirical distribution parameters. With the empirical bit probabilities, the multiple Bernoulli model gives a good approximation of the empirical mean, but the distribution width is too small. Conversely, the use of a Gaussian to model the query and database fingerprints allows to the hypergeometric/Gaussian model to reproduce the empirical distribution width, though the distribution mean is smaller than the empirical value.