Department of Statistics
STATISTICAL COLLOQUIUM
Concept of Sub-Independence
Speaker: Dr. G.G. Hamedani, Professor
Department of Mathematics, Statistics and Computer Science
Marquette University
Milwaukee, WI 53201-1881
Date: Friday, November 9, 2012 Time: 3:45 PM - 5:00 PM Room: GC 279B
Abstract
Limit theorems as well as other well-known results in probability and statistics are often based on the distribution of the sums of independent (and often identically distributed) random variables than the joint distribution of the summands. Therefore, the full force of independence of summands will not be required. In other words, it is the convolution of the marginal distributions which is needed, rather than the joint distribution of the summands which, in the case of independence, is the product of the marginal distributions. The concept of sub-independence is based on the convolution of the distributions and clearly is much weaker than that of independence. It is shown that the concept of sub-independence will be sufficient to yield the conclusions of these well-known theorems and results. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness.