NumCosmoDataClusterMassRichCount

Cluster mass-richness data object using true (integer) richness counts.

NcDataClusterMassRichCount is a data object analogous to NcDataClusterMassRich, but for the case where the richness is the actual (integer) number of galaxies detected in a cluster, rather than a continuous proxy already marginalized over projection effects. The observed count $N$ is modeled as a Poisson realization of a rate $\lambda$ that is itself log-normally distributed, i.e., $$ N \sim \text{Poisson}(\lambda), \quad \ln\lambda \sim \mathcal{N}(\mu(\ln M, z), \sigma(\ln M, z)), $$ where $\mu$ and $\sigma$ are provided by a NcClusterMassRichness model. The resulting Poisson-Lognormal probability $P(N \mid \mu,\sigma)$ is evaluated using NcmPLN1D.

If the mass-richness model’s cut parameter (see nc_cluster_mass_richness_get_cut()) is non-zero, each cluster’s probability is conditioned on $N \geq N_{\rm cut}$, with $N_{\rm cut} = \mathrm{round}(e^{\rm cut})$, mirroring the truncation applied by NcDataClusterMassRich for the continuous case.