Research for Queuing Theory

The exact distribution is given for the number of times the vertical steps of an empirical distribution cross the underlying theoretical distribution. The statistic was used for Smirnov [1] to derive limiting distributions of statistics used in Kolmogorov-Smirnov tests, and may be used as a goodness-of-fit test in its own right.

This research contribution addresses the problem of explicitly taking into account uncertainty about the demand for spare parts in making inventory procurement and stockage decisions. The model described provides for a unified treatment of the closely related problems of statistical estimation of demand and resource allocation within the inventory system, and leads to an easily implemented, efficient method of determining requirements for spare parts both in the early provisioning phase and in later periods of operations when demand data has accumulated.

This paper considers the estimation of multinomial probability vectors when only the sum of several multinomial processes is observed, and when the number of individuals governed by each process is known. The relationship of this problem to the previous literature is discussed, the likelihood function is given, the identification problem is also considered, and an algorithm is proposed for finding maximum likelihood estimators.

Comment on a proposed new estimator of the large sample asymptotic covariance matrix for the limited information maximum likelihood estimator in simultaneous equations.