Poisson limits for a clustering model of strauss
Keyword(s):
In this article we present a limiting result for the random variable Yn(r) which arises in a clustering model of Strauss (1975). The result is that under some sparseness-of-points conditions the process {Yn(r): 0 ≦ r ≦ r∞} converges weakly to a non-homogeneous Poisson process {Y(r): 0 ≦ r ≦ r∞} when n → ∞. Simulation results are given to indicate the accuracy of the approximation when n is moderate and applications of the limiting result to tests for clustering are discussed.
1977 ◽
Vol 14
(04)
◽
pp. 776-784
◽
2013 ◽
Vol 43
(1)
◽
pp. 44-71
2014 ◽
Vol 26
(2)
◽
pp. 171-183
◽
2010 ◽
Vol 5
(1)
◽
pp. 31-41
◽
1995 ◽
Vol 32
(03)
◽
pp. 707-726
◽
2003 ◽
Vol 19
(2)
◽
pp. 171-181
◽
2007 ◽
Vol 92
(2)
◽
pp. 243-251
◽
1969 ◽
Vol 6
(03)
◽
pp. 692-699
◽