Title: The best fit for the observed galaxy Counts-in-Cell distribution function,
Abstract: The Sloan Digital Sky Survey (SDSS) is the first dense redshift survey
encompassing a volume large enough to find the best analytic probability
density function that fits the galaxy Counts-in-Cells distribution $f_V(N)$,
the frequency distribution of galaxy counts in a volume $V$. Different analytic
functions have been previously proposed that can account for some of the
observed features of the observed frequency counts, but fail to provide an
overall good fit to this important statistical descriptor of the galaxy
large-scale distribution. Our goal is to find the probability density function
that better fits the observed Counts-in-Cells distribution $f_V(N)$. We have
made a systematic study of this function applied to several samples drawn from
the SDSS. We show the effective ways to deal with incompleteness of the sample
(masked data) in the calculation of $f_V(N)$. We use LasDamas simulations to
estimate the errors in the calculation. We test four different distribution
functions to find the best fit: the Gravitational Quasi-Equilibrium
distribution, the Negative Binomial Distribution, the Log Normal distribution
and the Log Normal Distribution including a bias parameter. In the two latter
cases, we apply a shot-noise correction to the distributions assuming the local
Poisson model. We show that the best fit for the Counts-in-Cells distribution
function is provided by the Negative Binomial distribution. In addition, at
large scales the Log Normal distribution modified with the inclusion of the
bias term also performs a satisfactory fit of the empirical values of $f_V(N)$.
Our results demonstrate that the inclusion of a bias term in the Log Normal
distribution is necessary to fit the observed galaxy Count-in-Cells
distribution function.