DISTRIBUTION FUNCTION OF DISTANCE BETWEEN TWO POINTS AND CHORD LENGTH FOR BOUNDED SMOOTH CONVEX DOMAINS
DOI:
https://doi.org/10.52575/2687-0959-2022-54-1-21-27Keywords:
chord length, bounded convex domain, distribution, distance between two points, density functions, explicit form, of the distance density functionAbstract
In the paper we consider the distribution functions of two independent and uniformly distributed random points, as well as the chord length in a bounded convex domain D. Using a number of known facts, we derive the explicit form of the distribution functions of the chord length and density for bounded convex bodies with a smooth boundary, as well as the explicit form of the density function of the distance between two points.
Downloads
References
Aharonyan N. G. 2015. The distribution of the distance between two random points in a convex set. Russian journal of mathematical research, 1(1): 4-8.
Ambartzumian R. V. 1990. Factorization Calculus and Geometric Probability (Encyclopedia Math. Appl. 33). Cambridge University Press, 286.
Geciauskas E. 1977. The distribution function of the distance between two points in a convex domain. Adv. Appl. Prob., 9: 472-478.
GilleW.. 1988. The chord length distribution of parallelepipeds with their limiting cases. Exp. Techn. Phys., 36: 197–208.
Harutyunyan H. S., Ohanyan V. K. 2009. Chord length distribution function for regular polygon. Exp. Techn. Phys., 42(2): 358–366.
Harutyunyan H. S., Ohanyan V. K. 2011. Chord length distribution function for convex polygons. SUTRA international journal mathematical science education, 4(2): 1-15.
Harutyunyan H. S., Ohanyan V. K. 2014. Orientation-dependent section distributions for convex bodies. Journal of contemporary mathematical analysis, 49(3): 139-156.
Santalo L .A.. 2004. Integral Geometry and Geometric Probability . Encyclopedia of Mathematics and its Applications, Addison-Wesley, MA, 486.
Stoyan D., Stoyan H. 1994. Fractals random shapes and point fields. John Wiley & Sons, Chichester, New-York.
Sulanke R. 1961. Die Verteilung der Sehnenl¨angen an Ebenen und r¨aumlichen Figuren. Math. Nachr, 22: 51–74.
Abstract views: 234
##submission.share##
Published
How to Cite
Issue
Section
Copyright (c) 2022 Applied Mathematics & Physics
This work is licensed under a Creative Commons Attribution 4.0 International License.
