On Sums of Random Variables and Independence
- 1 August 1986
- journal article
- Published by Taylor & Francis in The American Statistician
- Vol. 40 (3) , 214-215
- https://doi.org/10.1080/00031305.1986.10475395
Abstract
Suppose that the density of the sum of two random variables X and Y is given by the convolution of the two marginal densities. Although this condition is stronger than uncorrelatedness of X and Y, it does not imply stochastic independence, as is shown by three examples. A situation for which this fact may be relevant occurs in the construction of chi-squared tests for nested hypotheses.Keywords
This publication has 2 references indexed in Scilit:
- Misspecifications of the Normal DistributionThe American Statistician, 1982
- Non-Normal Bivariate Distributions with Normal MarginalsThe American Statistician, 1973