On joint probability distribution of the number of vertices and area of the convex hulls generated by a Poisson point process

Sh.K. Formanov and I.M. Khamdamov

Statistics & Probability Letters, 2021, vol. 169, issue C

Abstract: Consider a convex hull generated by a homogeneous Poisson point process in a cone in the plane. In the present paper the central limit theorem is proved for the joint probability distribution of the number of vertices and the area of a convex hull in a cone bounded by the disk of radius T (the center of the disk is at the cone vertex), for T→∞. From the results of the present paper the previously known results of Groeneboom (1988) and Cabo and Groeneboom (1994) are followed, in which the central limit theorem was proved for the number of vertices and the area of the convex hull in a square by approximating the binomial point process by a homogeneous Poisson point process.

Keywords: Convex hull; Random point; Poisson point process (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715220302698
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:169:y:2021:i:c:s0167715220302698

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2020.108966

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().