clenspy.selection.richness_kernel.richness_pdf

clenspy.selection.richness_kernel.richness_pdf(x, lambda_true, z, params)

\(P(\lambda^{\rm ob}\mid\lambda^{\rm tr},z)\), the full mixture.

\[P = (1-f^{\rm prj})\,\mathcal N(x;\mu,\sigma) + f^{\rm prj}\,p_{\rm EMG}(x;\mu,\sigma,\tau)\]

NOTE: a density. Its bin integral is richness_bin_probability, which is analytic – this function exists for the places that genuinely need the density at a point, notably the \(\lambda^{\rm tr}\) marginalisation inside \(b_{\rm sel}\).