On the Structural Properties of the Conditional Distributions
- 1 June 1967
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 10 (2) , 239-245
- https://doi.org/10.4153/cmb-1967-022-2
Abstract
If x, x1,…, xn are independent stochastic variables and if the conditional distribution of x given x1 +…+ xn is known, what can be said about the marginal distributions of x, x1,…, xn? In this paper we will show that if the conditional distribution of x given a subset of x1, x2,…, xn-1, x+ x1 +…+ xn has a certain structural form then x, x1,…, xn are distributed as members of the linear exponential family of distributions and further x1,…, xn are identically distributed.Keywords
This publication has 2 references indexed in Scilit:
- On the Laws of Cauchy and GaussThe Annals of Mathematical Statistics, 1959
- A characteristic property of the Poisson distributionMathematical Proceedings of the Cambridge Philosophical Society, 1952