A joint characterization of the multinomial distribution and the Poisson process
1983 ◽
Vol 20
(01)
◽
pp. 202-208
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Keyword(s):
It has been recently proved that if N, X 1, X 2, … are non-constant mutually independent random variables with X 1,X 2, … identically distributed and N non-negative and integer-valued, then the independence of and implies that X 1 is Bernoulli and N is Poisson. A well-known theorem in point process theory due to Fichtner characterizes a Poisson process in terms of a sum of independent thinnings. In the present article, simultaneous generalizations of both of these results are provided, including a joint characterization of the multinomial distribution and the Poisson process.
Keyword(s):
1981 ◽
Vol 18
(03)
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pp. 652-659
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On the probability that a random point is the jth nearest neighbour to its own kth nearest neighbour
1986 ◽
Vol 23
(01)
◽
pp. 221-226
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1992 ◽
Vol 112
(3)
◽
pp. 613-629
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