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Halo Occupation Distribution (HOD) models help us to connect observations andtheory, by assigning galaxies to dark matter haloes. In this work we study oneof the components of HOD models: the probability distribution function (PDF),which is used to assign a discrete number of galaxies to a halo, given a meannumber of galaxies. For satellite galaxies, the most commonly used PDF is aPoisson Distribution. PDFs with super-Poisson variances have also been studied,allowing for continuous values of variances. This has not been the case forsub-Poisson variances, for which only the Nearest Integer distribution, with asingle variance, has been used in the past. In this work we propose adistribution based on the binomial one, which provides continuous sub-Poissonvariances. We have generated mock galaxy catalogues from two dark-matter onlysimulations, UNIT and OUTERIM, with HOD models assuming different PDFs. We showthat the variance of the PDF for satellite galaxies affects the one-halo termof the projected correlation function, and the Count-In-Cells (CIC) one pointstatistics. We fit the clustering of eBOSS Emission Line Galaxies, finding apreference for a sub-poissonian PDF, when we only vary the parametercontrolling the PDF variance and the fraction of satellites. Using a mockcatalogue as a reference, we have also included both the clustering and CIC toconstrain the parameters of the HOD model. CIC can provide strong constraintsto the PDF variance of satellite galaxies.

Improving and extending non-Poissonian distributions for satellite galaxies sampling in HOD: applications to eBOSS ELGs