On a characterization of Poisson distribution
Keyword(s):
Recently Rao (1963) has considered discrete models where an original observation produced by nature is subjected to a destructive process and we observe the undestroyed part of the original observation. Suppose the original observation produced by nature is distributed according to a Poisson distribution with parameter λ and the probability that the original observation n is reduced to r due to the destructive process is Now if Y denotes the resulting random variable (r.v.), then it is easily seen that Let us call this condition the *-condition. Later Rao and Rubin ({1964),Theorem 1) proved that the *-condition is a characterizing property of the Poisson distribution.
1970 ◽
Vol 7
(02)
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pp. 497-501
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1972 ◽
Vol 71
(3)
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pp. 517-522
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1986 ◽
Vol 100
(3)
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pp. 583-589
1999 ◽
Vol 31
(02)
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pp. 394-421
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1972 ◽
Vol 9
(04)
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pp. 852-856
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1999 ◽
Vol 31
(2)
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pp. 394-421
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