### Abstract

Colombi et al. (Paper I) investigated the counts-in-cells statistics and their respective errors in the τCDM Virgo Hubble Volume simulation. This extremely large N-body experiment also allows a numerical investigation of the cosmic distribution function, Y(Ã), itself for the first time. For a statistic A, Y(Ã) is the probability density of measuring the value Ã in a finite galaxy catalogue. Y was evaluated for the distribution of counts-in-cells, P_{N}, the factorial moments, F_{k}, and the cumulants, ξ̄ and S_{N}s, using the same subsamples as Paper I. While Paper I concentrated on the first two moments of Y, i.e. the mean, the cosmic error and the cross-correlations, here the function Y is studied in its full generality, including a preliminary analysis of joint distributions Y(Ã, B̃). The most significant, and reassuring result for the analyses of future galaxy data is that the cosmic distribution function is nearly Gaussian provided its variance is small. A good practical criterion for the relative cosmic error is that ΔA/A ≲ 0.2. This means that for accurate measurements, the theory of the cosmic errors, presented by Szapudi & Colombi and Szapudi, Colombi & Bernardeau, and confirmed empirically by Paper I, is sufficient for a full statistical description and thus for a maximum likelihood rating of models. As the cosmic error increases, the cosmic distribution function Y becomes increasingly skewed and is well described by a generalization of the lognormal distribution. The cosmic skewness is introduced as an additional free parameter. The deviation from Gaussianity of Y(F̃_{k}) and Y(S̃_{N}) increases with order k, N and similarly for Y(P̃_{N}) when N is far from the maximum of P_{N}, or when the scale approaches the size of the catalogue. For our particular experiment, Y(F̃_{k}) and Y(ξ≃) are well approximated with the standard lognormal distribution, as evidenced by both the distribution itself and the comparison of the measured skewness with that of the lognormal distribution.

Original language | English |
---|---|

Pages (from-to) | 725-733 |

Number of pages | 9 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 313 |

Issue number | 4 |

Publication status | Published - Apr 21 2000 |

### Fingerprint

### Keywords

- Galaxies: Clusters: General
- Large-scale structure of Universe
- Methods: Numerical
- Methods: Statistical

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Monthly Notices of the Royal Astronomical Society*,

*313*(4), 725-733.

**Experimental cosmic statistics - II. Distribution.** / Szapudi, I.; Colombi, Stéphane; Jenkins, Adrian; Colberg, Jörg.

Research output: Contribution to journal › Article

*Monthly Notices of the Royal Astronomical Society*, vol. 313, no. 4, pp. 725-733.

}

TY - JOUR

T1 - Experimental cosmic statistics - II. Distribution

AU - Szapudi, I.

AU - Colombi, Stéphane

AU - Jenkins, Adrian

AU - Colberg, Jörg

PY - 2000/4/21

Y1 - 2000/4/21

N2 - Colombi et al. (Paper I) investigated the counts-in-cells statistics and their respective errors in the τCDM Virgo Hubble Volume simulation. This extremely large N-body experiment also allows a numerical investigation of the cosmic distribution function, Y(Ã), itself for the first time. For a statistic A, Y(Ã) is the probability density of measuring the value Ã in a finite galaxy catalogue. Y was evaluated for the distribution of counts-in-cells, PN, the factorial moments, Fk, and the cumulants, ξ̄ and SNs, using the same subsamples as Paper I. While Paper I concentrated on the first two moments of Y, i.e. the mean, the cosmic error and the cross-correlations, here the function Y is studied in its full generality, including a preliminary analysis of joint distributions Y(Ã, B̃). The most significant, and reassuring result for the analyses of future galaxy data is that the cosmic distribution function is nearly Gaussian provided its variance is small. A good practical criterion for the relative cosmic error is that ΔA/A ≲ 0.2. This means that for accurate measurements, the theory of the cosmic errors, presented by Szapudi & Colombi and Szapudi, Colombi & Bernardeau, and confirmed empirically by Paper I, is sufficient for a full statistical description and thus for a maximum likelihood rating of models. As the cosmic error increases, the cosmic distribution function Y becomes increasingly skewed and is well described by a generalization of the lognormal distribution. The cosmic skewness is introduced as an additional free parameter. The deviation from Gaussianity of Y(F̃k) and Y(S̃N) increases with order k, N and similarly for Y(P̃N) when N is far from the maximum of PN, or when the scale approaches the size of the catalogue. For our particular experiment, Y(F̃k) and Y(ξ≃) are well approximated with the standard lognormal distribution, as evidenced by both the distribution itself and the comparison of the measured skewness with that of the lognormal distribution.

AB - Colombi et al. (Paper I) investigated the counts-in-cells statistics and their respective errors in the τCDM Virgo Hubble Volume simulation. This extremely large N-body experiment also allows a numerical investigation of the cosmic distribution function, Y(Ã), itself for the first time. For a statistic A, Y(Ã) is the probability density of measuring the value Ã in a finite galaxy catalogue. Y was evaluated for the distribution of counts-in-cells, PN, the factorial moments, Fk, and the cumulants, ξ̄ and SNs, using the same subsamples as Paper I. While Paper I concentrated on the first two moments of Y, i.e. the mean, the cosmic error and the cross-correlations, here the function Y is studied in its full generality, including a preliminary analysis of joint distributions Y(Ã, B̃). The most significant, and reassuring result for the analyses of future galaxy data is that the cosmic distribution function is nearly Gaussian provided its variance is small. A good practical criterion for the relative cosmic error is that ΔA/A ≲ 0.2. This means that for accurate measurements, the theory of the cosmic errors, presented by Szapudi & Colombi and Szapudi, Colombi & Bernardeau, and confirmed empirically by Paper I, is sufficient for a full statistical description and thus for a maximum likelihood rating of models. As the cosmic error increases, the cosmic distribution function Y becomes increasingly skewed and is well described by a generalization of the lognormal distribution. The cosmic skewness is introduced as an additional free parameter. The deviation from Gaussianity of Y(F̃k) and Y(S̃N) increases with order k, N and similarly for Y(P̃N) when N is far from the maximum of PN, or when the scale approaches the size of the catalogue. For our particular experiment, Y(F̃k) and Y(ξ≃) are well approximated with the standard lognormal distribution, as evidenced by both the distribution itself and the comparison of the measured skewness with that of the lognormal distribution.

KW - Galaxies: Clusters: General

KW - Large-scale structure of Universe

KW - Methods: Numerical

KW - Methods: Statistical

UR - http://www.scopus.com/inward/record.url?scp=0041970250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041970250&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041970250

VL - 313

SP - 725

EP - 733

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 4

ER -