The probability density function of an area covered with disks whose centers are randomly distributed

References

• Garwood , F. 1947 . The variance of the overlap of geometrical figures with reference to a bombing problem . Biometrika , 34 : 1 – 17 .
   PubMed Web of Science ®Google Scholar
• Getis , A. and Boots , B. 1978 . Models of Spatial Processes , Cambrige University Press .
   Google Scholar
• Green , P.J. and Sibson , R. 1978 . Computing Dirichlet tessellation in the plane . The Computer Journal , 21 : 168 – 173 .
   Web of Science ®Google Scholar
• Guenther , W.C. and Terragno , P.J. 1964 . A review of the literature of a class of coverage problems . Annals of Mathematical Statistics , 35 : 232 – 260 .
   Google Scholar
• Holst , L. 1981 . On convergence of the coverage by random arcs on a circle and the largest spacing . Annals of Probability , 9 : 648 – 655 .
   Google Scholar
• Horspool , R.N. 1979 . “ Constructing the Voronoi diagram in the plane ” . In Technical Report , McGill University .
   Google Scholar
• Husler , J. 1982 . Random coverage of the circle and asymptotic distributions . Journal of Applied Probability , 19 : 578 – 587 .
   Google Scholar
• Janson , S. 1984 . “ Doctoral dissertation, Department of Mathematics ” . In Random Coverings and Related Problems , Uppsala University .
   Google Scholar
• Kaplan , N. 1978 . A limit theorem for random coverings of a circle which do not quite cover . Journal of Applied Probability , 15 : 443 – 446 .
   Google Scholar
• Kendall , M.G. and Moran , P.A.P. 1963 . Geometrical Probability , London : Charles Griffin .
   Google Scholar
• Ohya , T. , Iri , M. and Murota , K. 1984 . A fast Voronoi diagram algorithm with quaternary tree bucketing . Information Processing Letter , 18 : 227 – 231 .
   Web of Science ®Google Scholar
• Ohya , T. , Iri , M. and Murota , K. 1984 . Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms . Journal of the Operations Research Society of Japan , 27 : 306 – 337 .
   Google Scholar
• Okabe , A. and Miki , F. 1984 . A conditional nearest-neighbour spatial association measure for the analysis of conditional locational interdependence . Environment and Planning , 16 : 163 – 171 .
   Web of Science ®Google Scholar
• Rhynsburger , D. 1973 . Analytic delineation of Thiessen polygons . Geographical Analysis , 5 : 133 – 144 .
   Web of Science ®Google Scholar
• Roach , S.A. 1968 . The Theory of Random Clumping , London : Methuen .
   Google Scholar
• Robbins , H.E. 1944 . On the measure of a random set . Annals of Mathematical Statistics , 15 : 70 – 74 .
   Google Scholar
• Robbins , H.E. 1945 . On the measure of a random set. II . Annals of Mathematical Statistics , 16 : 342 – 347 .
   Google Scholar
• Salzer , H.E. 1951 . Checking and interpolation of functions tabulated at certain irregular logarithmic intervals . Journal of Research of National Bureau of Standards , 46 : 74 – 77 .
   Google Scholar
• Santalo , L.A. 1947 . On the first two moments of the measure of a random set . Annals of Mathematical Statistics , 18 : 37 – 49 .
   Google Scholar
• Santalo , L.A. 1976 . Integral Geometry and Geometric Probability , Mass, Addison-Wesley : Reading .
   Google Scholar
• Shamos , M.I. and Hoey , D. 1975 . “ Closest-point problems ” . In Proceedings of the 16th Annual IEEE Symposium on Foundations of Computer Science 151 – 162 .
   Google Scholar
• Siegel , A.F. 1979 . Asymptotic coverage distributions on the circle . Annals of Probability , 7 : 651 – 661 .
   Web of Science ®Google Scholar
• Siegel , A.F. and Holst , L. 1982 . Covering the circle with random arcs of random size . Journal of Applied Probability , 19 : 373 – 381 .
   Google Scholar