In probability theory, Raikov’s theorem, named after Dmitry Raikov, states that if the sum of two independent non-negative random variables X and Y has a Poisson distribution, then both X and Y themselves must have the Poisson distribution. It says the same thing about the Poisson distribution that Cramér's theorem says about the normal distribution. It can readily be shown by mathematical induction that the same is true of the sum of more than two independent random variables.
Notes and references
- D. Raikov (1937). "On the decomposition of Poisson laws". C. R. (Doklady) Academy of Sciences of URSS 14: 9–11.
- Johnson, N.L., Kotz, S., Kemp, A.W. (1993) Univariate Discrete Distributions, Wiley. p. 173 ISBN 0-471-54897-9
- Galambos, Janos (2006) Raikov's theorem, in Encyclopedia of Statistical Sciences, Wiley. doi:10.1002/0471667196.ess2160.pub2