Sub-Independence: A Useful Concept

G.G. Hamedani and Mehdi Maadooliat
Department of Mathematics, Statistics and Computer Science, Marquette University, WI, USM

Series: Mathematics Research Developments
BISAC: COM014000



Volume 10

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Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick


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The concept of sub-independence is defined in terms of the convolution of the distributions of random variables, providing a stronger sense of dissociation between random variables than that of uncorrelatedness. If statistical tests reject independence but not lack of correlation, a model with sub-independent components can be appropriate to determine the distribution of the sum of the random variables.

This monograph presents most of the important classical results in probability and statistics based on the concept of sub-independence. This concept is much weaker than that of independence and yet can replace independence in most limit theorems as well as well-known results in probability and statistics. This monograph, the first of its kind on the concept of sub-independence, should appeal to researchers in applied sciences where the lack of independence of the uncorrelated random variables may be apparent but the distribution of their sum may not be tractable.


Chapter 1 - Introduction (pp. 1-12)

Chapter 2 - Some Results on Characterizations Based on the Concept of Sub-Independence (pp. 13-44)

Chapter 3 - Central Limit Theorem and Equivalence of Sub-Independence (pp. 45-66)


About the Authors


Audience: Graduate Students; Probability and Statistics Instructors at Graduate Level; All academicians who will be employing advanced probability and statistics in their research areas; The probabilists and/or statisticians who work in industries; Biostatisticians.

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