Another characteristic property of the Poisson distribution
1970 ◽
Vol 68
(1)
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pp. 167-169
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Keyword(s):
1. Introduction: In (4) Moran considers two independent random variables X and Y taking non-negative integral values to give a characterization of the Poisson distribution. He establishes that the conditional distribution of X, given the total X + Y, is binomial for all given values of X + Y and there exists at least one i so that P(x = i) > 0, P( Y = i) > 0 if and only if X and Y have Poisson distributions. A slightly improved version of this result is given by Chatterji (1). For a comprehensive bibliography on the Poisson distribution the reader is referred to (3).
1972 ◽
Vol 9
(04)
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pp. 852-856
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1981 ◽
Vol 18
(01)
◽
pp. 316-320
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2010 ◽
Vol 88
(1)
◽
pp. 93-102
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1983 ◽
Vol 20
(01)
◽
pp. 202-208
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1981 ◽
Vol 18
(03)
◽
pp. 652-659
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