Accession Number : AD0619189

Title :   A STOCHASTIC MODEL FOR TIME CHANGES IN A BINARY DYADIC RELATION, WITH APPLICATION TO GROUP DYNAMICS.

Descriptive Note : Doctoral thesis,

Corporate Author : MICHIGAN STATE UNIV EAST LANSING

Personal Author(s) : Bhargava,T. N.

Report Date : 11 JUN 1962

Pagination or Media Count : 173

Abstract : This thesis is concerned with the development of a stochastic model for analyzing time changes in a binary dyadic relation over a finite set of points. For purposes of drawing statistical inference in time the total relation R (A) on the set A is looked upon as an aggregate of its subrelations on subsets of the set A. The number of states in which a subrelation may be found, at any time, is very large; consequently three classification schemes are described to obtain a small number of mutually exclusive and exhaustive classes. Methods are presented to enumerate the number of subrelations of R (A) in various states at any time, and to count the number of transitions from one state to another in time. The process of change in the total relation over time is described as a timedependent process, and some statistical tests to determine the nature of the dependence are given. Certain aspects of the probability distributions of the random variables R sub ni (number of n-point subrelations of R (A) in state s'i) are discussed in the second part of the thesis. It is shown that the probability distributions of R sub ni may be approximated by Poisson distributions. Finally an application of the model to group dynamics is described and empirical examination of Markov properties is made for a particular set of data. (Author)

Descriptors :   (*STOCHASTIC PROCESSES, GROUP DYNAMICS), (*GROUP DYNAMICS, STOCHASTIC PROCESSES), MATHEMATICAL MODELS, BINARY ARITHMETIC, DISTRIBUTION THEORY, PSYCHOLOGICAL TESTS

Distribution Statement : APPROVED FOR PUBLIC RELEASE