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Expected measure of the union of random rectangles

Part of: Geometric probability and stochastic geometry Approximations and expansions

Published online by Cambridge University Press:  14 July 2016

Chern-Ching Chao ,
Hsien-Kuei Hwang  and
Wen-Qi Liang
Chern-Ching Chao*
Affiliation:
Academia Sinica
Hsien-Kuei Hwang*
Affiliation:
Academia Sinica
Wen-Qi Liang*
Affiliation:
Academia Sinica
*
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan.
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan.
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan.
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Abstract

An asymptotic expression for the expected area of the union of n random rectangles is derived by Mellin transforms, where their two diagonal corners are independently and uniformly distributed over (0,1)2. The general result for d-dimensional hyper-rectangles is also stated.

Keywords

Computational geometryconvex hullgeometric probabilitygeometry of rectanglesMellin transformcalculus of finite difference

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 495 - 500
Copyright
Copyright © Applied Probability Trust 1998 

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