A Poisson limit theorem for weakly exchangeable events
Keyword(s):
Let Y1, Y2, · ·· be a sequence of independent, identically distributed random variables, g some symmetric 0–1 function of m variables and set Silverman and Brown (1978) have shown that under certain conditions the statistic is asymptotically distributed as a Poisson random variable. They then use this result to derive limit distributions for various statistics, useful in the analysis of spatial data. In this paper, it is shown that Silverman and Brown's theorem holds under much weaker assumptions; assumptions which involve only the symmetry of the joint distributions of the Xil…im.
1979 ◽
Vol 16
(04)
◽
pp. 794-802
◽
1983 ◽
Vol 20
(01)
◽
pp. 47-60
◽
1966 ◽
Vol 3
(01)
◽
pp. 272-273
◽
1983 ◽
Vol 15
(03)
◽
pp. 585-600
◽
1979 ◽
Vol 86
(2)
◽
pp. 301-312
◽
2021 ◽
Vol 73
(1)
◽
pp. 62-67