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eduardojsbarroso committed Mar 2, 2023
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"\n",
"## Data\n",
"\n",
"The data was generated with the NumCosmo library. We used the [Tinker08](https://arxiv.org/abs/0803.2706) mass function with critical overdensity $\\Delta_c = 200$. We generated a catalog of clusters with a given mass, redshift and richness. We can use the mass function to generate clusters with a given a mass at a given redshift, but to generate its richness, we used the richness-mass relation described in [Murata et al](https://arxiv.org/abs/1707.01907). Explictly, the probability of a cluster with mass $M$ at redshift $z$ having a richness $ln \\lambda$ is given by\n",
"The data was generated with the NumCosmo library. We used the [Tinker08](https://arxiv.org/abs/0803.2706) mass function with mean overdensity $\\Delta_m = 200$. We generated a catalog of clusters with a given mass, redshift and richness. We can use the mass function to generate clusters with a given a mass at a given redshift, but to generate its richness, we used the richness-mass relation described in [Murata et al](https://arxiv.org/abs/1707.01907). Explictly, the probability of a cluster with mass $M$ at redshift $z$ having a richness $ln \\lambda$ is given by\n",
"$$$$\n",
"\\begin{align}\n",
"P(\\ln \\lambda \\mid M, z)=\\frac{1}{\\sqrt{2 \\pi} \\sigma_{\\ln \\lambda \\mid M, z}} \\exp \\left(-\\frac{x^2(\\lambda, M, z)}{2 \\sigma_{\\ln \\lambda \\mid M, z}^2}\\right),\n",
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