Chandrasekhar, S.
(1949)
*On a class of probability distributions*
Mathematical Proceedings of the Cambridge Philosophical Society, 45
(2).
pp. 219-224.
ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0305004100024749

## Abstract

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 F=Σ^{∞}_{j=1}r_{j}/r^{n+1}_{j}(|r_{j}|=r_{j}),
where the r_{j}'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 n>3/2 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.

Item Type: | Article |
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Source: | Copyright of this article belongs to Cambridge University Press. |

ID Code: | 70704 |

Deposited On: | 19 Nov 2011 10:04 |

Last Modified: | 19 Nov 2011 10:04 |

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