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On a class of probability distributions

Published online by Cambridge University Press:  24 October 2008

S. Chandrasekhar
S. Chandrasekhar
Affiliation:
Yerkes ObservatoryWilliams Bay, Wisconsin
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Extract

1. The statement of the problem. A problem which arises in certain physical (5) and astronomical (1, 3) contexts relates to the probability distribution of the infinite sum

where the rj's are the position vectors from a fixed origin of an infinite uniform Poisson distribution of points with a given constant mean space density N. While certain special cases of the sum (1) have been considered in the literature (cf. (2)) the study of the general case discloses properties of a class of probability distributions which appear to have some interest. For example, we shall show that the probability distribution of F exists only for that the moments of F (= |F|) exist only for orders 0 ≤ p < 3/n, and finally that an explicit formula can be given for all the finite moments.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 219 - 224
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

(1)Chandrasekhar, S.Astrophys. J. 94 (1941), 511.CrossRefGoogle Scholar
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