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This paper considers the statistical inference of structural properties in organizations. Specifically, the sampling probability distributions of the number of links and the cumulative distribution of the number of components are determined. Probability estimates of both the number of links and the number of components are then found. [ABSTRACT FROM AUTHOR]

The intent of this paper is to provide a definition of a sociometric clique in the language of graph theory. This problem is viewed from two perspectives: maintaining fidelity to the intuitive notion of a clique; and providing adequate computational mechanics for large bodies of data. Luce's (1950) concept of an n-clique is used, but further qualifications are added. Two statistics or measures with associated probability distributions are defined for testing the adequacy of a subgraph which qualifies according to the definition. [ABSTRACT FROM AUTHOR]

This paper compares three methods (sequel, cardinal, maximal) for constructing a weak order from a partial order on a finite set. The constructed weak orders include the partial order. To evaluate the methods, several different selection disciplines were used to stochastically generate partial orders from a fixed linear order. The error of a weak order which includes a generated partial order is a function of the number of ordered pairs added to the partial order to get the weak order which are the reverse of ordered pairs in the fixed linear order. In all cases, the sequel and cardinal mean errors were much lower than the maximal mean error. In most but not all cases, the cardinal mean error was lower than the sequel mean error. [ABSTRACT FROM AUTHOR]

This paper proposes a continuous time version of a diffusion model introduced by Gray and von Broembsen (1974). The new formulation allows a deeper analysis of the stochastic aspects of the diffusion process and, in particular, of the threshold effect which occurs in the absence of an outside transmitting source. Attention is drawn to important similarities and differences between the stochastic and the deterministic versions of the model. Simple approximations for the distribution of the ultimate number of hearers axe given as well as the exact distribution. Some generalizations are suggested and it is shown that their analysis in deterministic terms is relatively easy. [ABSTRACT FROM AUTHOR]

A mathematical model of friendship choice distribution is proposed. The model differs from other models in that it takes into account certain structural factors in sociometric relations. Two theoretical distributions are derived from a set of assumptions as two approximations to satisfy those assumptions. One distribution is a well-known negative binomial distribution, but its derivation is new. The other distribution has an unfamiliar mathematical structure but it shares certain features with the negative binomial distribution. The two parameters of these distributions are regarded as measures of the degree of expansiveness and the degree of local cohesiveness of friendship ties. The model is tested with several sets of empirical data and shows usefulness as a descriptive tool. [ABSTRACT FROM AUTHOR]

A systematic procedure of truncating the hierarchy of moment equations describing the stochastic evolution of a Markov process in a finite population is developed. The procedure makes use of the asymptotic expression for a certain higher-order moment of the relevant probability distribution and yields finite-size corrections to all lower-order moments. The usefulness of the method is illustrated by applying it to study the mean and the variance of the stochastic variable n(t), the number of active spreaders at time t, in Bartholomew's model of diffusion of information. The results thus obtained are compared with the ones following from the exact probability distribution for the model (wherever known) and the agreement between the two sets of results is found to be remarkably good. [ABSTRACT FROM AUTHOR]