The best fit for the observed galaxy Counts-in-Cell distribution function

C. Pareja-Flores; Ll. Hurtado-Gil; M. J. Pons-Border\'ia; P. Arnalte-Mur; S. Paredes; V. J. Mart\'inez

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The best fit for the observed galaxy Counts-in-Cell distribution function

Ll. Hurtado-Gil, V. J. Martínez, P. Arnalte-Mur, M. J. Pons-Bordería, C. Pareja-Flores, S. Paredes

Cosmology and Nongalactic Astrophysics · Submitted 3 Mar 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the best fit for the Counts-in-Cells distribution function is provided by the Negative Binomial distribution.

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arXiv ID1703.01087 (version 2)

Pith ID3LKSWVCM, Pith's permanent record of this paper and its review

CitationC. Pareja-Flores, Ll. Hurtado-Gil, M. J. Pons-Border\'ia, P. Arnalte-Mur, S. Paredes, V. J. Mart\'inez. "The best fit for the observed galaxy Counts-in-Cell distribution function." arXiv:1703.01087 (2017). https://pith.science/paper/3LKSWVCM

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What the abstract itself states, as probabilities: claims first 0.62 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.87 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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 $V$.	background 0.92	0.21	0.03	asserted 1.00
s1	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.	gap 0.61	0.05	0.02	asserted 0.99
s2	Our goal is to find the probability density function that better fits the observed Counts-in-Cells distribution $f_V(N)$.	contribution 0.76	0.22	0.03	asserted 0.80
s3	We have made a systematic study of this function applied to several samples drawn from the SDSS.	contribution 0.70	0.95	0.02	asserted 0.97
s4	We show the effective ways to deal with incompleteness of the sample (masked data) in the calculation of $f_V(N)$.	method 0.95	0.90	0.02	asserted 1.00
s5	We use LasDamas simulations to estimate the errors in the calculation.	method 1.00	0.91	0.02	asserted 0.99
s6	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.	method 0.95	0.90	0.04	asserted 0.89
s7	In the two latter cases, we apply a shot-noise correction to the distributions assuming the local Poisson model.	method 1.00	0.88	0.02	asserted 0.97
s8	We show that the best fit for the Counts-in-Cells distribution function is provided by the Negative Binomial distribution.	result 1.00	0.96	0.91	asserted 1.00
s9	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 $f_V(N)$.	result 1.00	0.91	0.07	asserted 0.92
s10	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.	interpretation 0.71	0.89	0.25	asserted 1.00

What kind of paper the classifier reports this is: empirical study 0.97 · evidence from analysis of existing data 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original 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.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Dark Photon Oscillations in Our Inhomogeneous Universe
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9 arXiv papers cite this in 15 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 9 sentences without a confident label

Uses its data or values 1 paper

We will adopt the value of $b = 1.5$ below, consistent with Ref. [ref] .

Modeling Dark Photon Oscillations in Our Inhomogeneous Universe · Log-normal PDF with bias · 0.97

Cites it as support 1 paper

For $b > 1$, $δ_b$ can have downward fluctuations of up to $-b$, which are clearly unphysical; however, $𝒫_LN^b$ has been shown to be a reasonable fit to data [ref] , and we are once again using the PDF only as a way of capturing systematic uncertainties.

Modeling Dark Photon Oscillations in Our Inhomogeneous Universe · Log-normal PDF with bias · 0.97

Cites it as background 3 papers

Counts-in-cells statistics of galaxies have been extracted from observations in numerous works [ref] spanning data sets from IRAS over SDSS to VIPERS and DES science verification.

A question of separation: disentangling tracer bias and gravitational nonlinearity with counts-in-cells statistics · Introduction · 0.93
Pioneering observational work on the one-point statistics of galaxies was carried out by Hubble [ref] , and measurements of this observable have been made in more recent surveys [ref] .

The position-dependent matter density probability distribution function · Introduction · 0.95
Hubble [ref] and has been measured in galaxy surveys [ref] .

Renormalizing one-point probability distribution function for cosmological counts in cells · Introduction and Summary · 0.95

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