### Abstract

We studied some statistical properties of the spatial point process displayed by GRBs of known redshift. To find ring-like point patterns we developed an algorithm and defined parameters to characterize the level of compactness and regularity of the rings found in this procedure. Applying this algorithm to the GRB sample we identified three more ring-like point patterns. Although, they had the same regularity but much less level of compactness than the original GRB ring. Assuming a stochastic independence of the angular and radial positions of the GRBs we obtained 1502 additional samples, altogether 542 222 data points, by bootstrapping the original one. None of these data points participated in rings having similar level of compactness and regularity as the original one. Using an appropriate kernel we estimated the joint probability density of the angular and radial variables of the GRBs. Performing MCMC simulations we obtained 1502 new samples, altogether 542 222 data points. Among these data points only three represented ring-like patterns having similar parameters as the original one. By defining a new statistical variable we tested the independence of the angular and radial variables of the GRBs. We concluded that despite the existence of local irregularities in the GRBs' spatial distribution (e.g. the GGR) one cannot reject the Cosmological Principle, based on their spatial distribution as a whole. We pointed out the large-scale spatial pattern of the GRB activity does not necessarily reflects the large-scale distribution of the cosmic matter.

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

Pages (from-to) | 3169-3179 |

Number of pages | 11 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 473 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Gamma-rays: galaxies: clusters
- Large-scale structure of Univers
- Methods: statistical

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Monthly Notices of the Royal Astronomical Society*,

*473*(3), 3169-3179. https://doi.org/10.1093/mnras/stx2550

**Some statistical remarks on the giant GRB ring.** / Balázs, L.; Rejto, Lídia; Tusnády, Gábor.

Research output: Contribution to journal › Article

*Monthly Notices of the Royal Astronomical Society*, vol. 473, no. 3, pp. 3169-3179. https://doi.org/10.1093/mnras/stx2550

}

TY - JOUR

T1 - Some statistical remarks on the giant GRB ring

AU - Balázs, L.

AU - Rejto, Lídia

AU - Tusnády, Gábor

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We studied some statistical properties of the spatial point process displayed by GRBs of known redshift. To find ring-like point patterns we developed an algorithm and defined parameters to characterize the level of compactness and regularity of the rings found in this procedure. Applying this algorithm to the GRB sample we identified three more ring-like point patterns. Although, they had the same regularity but much less level of compactness than the original GRB ring. Assuming a stochastic independence of the angular and radial positions of the GRBs we obtained 1502 additional samples, altogether 542 222 data points, by bootstrapping the original one. None of these data points participated in rings having similar level of compactness and regularity as the original one. Using an appropriate kernel we estimated the joint probability density of the angular and radial variables of the GRBs. Performing MCMC simulations we obtained 1502 new samples, altogether 542 222 data points. Among these data points only three represented ring-like patterns having similar parameters as the original one. By defining a new statistical variable we tested the independence of the angular and radial variables of the GRBs. We concluded that despite the existence of local irregularities in the GRBs' spatial distribution (e.g. the GGR) one cannot reject the Cosmological Principle, based on their spatial distribution as a whole. We pointed out the large-scale spatial pattern of the GRB activity does not necessarily reflects the large-scale distribution of the cosmic matter.

AB - We studied some statistical properties of the spatial point process displayed by GRBs of known redshift. To find ring-like point patterns we developed an algorithm and defined parameters to characterize the level of compactness and regularity of the rings found in this procedure. Applying this algorithm to the GRB sample we identified three more ring-like point patterns. Although, they had the same regularity but much less level of compactness than the original GRB ring. Assuming a stochastic independence of the angular and radial positions of the GRBs we obtained 1502 additional samples, altogether 542 222 data points, by bootstrapping the original one. None of these data points participated in rings having similar level of compactness and regularity as the original one. Using an appropriate kernel we estimated the joint probability density of the angular and radial variables of the GRBs. Performing MCMC simulations we obtained 1502 new samples, altogether 542 222 data points. Among these data points only three represented ring-like patterns having similar parameters as the original one. By defining a new statistical variable we tested the independence of the angular and radial variables of the GRBs. We concluded that despite the existence of local irregularities in the GRBs' spatial distribution (e.g. the GGR) one cannot reject the Cosmological Principle, based on their spatial distribution as a whole. We pointed out the large-scale spatial pattern of the GRB activity does not necessarily reflects the large-scale distribution of the cosmic matter.

KW - Gamma-rays: galaxies: clusters

KW - Large-scale structure of Univers

KW - Methods: statistical

UR - http://www.scopus.com/inward/record.url?scp=85041066970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041066970&partnerID=8YFLogxK

U2 - 10.1093/mnras/stx2550

DO - 10.1093/mnras/stx2550

M3 - Article

AN - SCOPUS:85041066970

VL - 473

SP - 3169

EP - 3179

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 3

ER -