Research for Stochastic Processes

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A BAYESIAN APPROACH TO DEMAND ESTIMATION AND INVENTORY PROVISIONING
August 1, 1974
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.
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ON A THEOREM OF WEYL
June 1, 1974
If A is a Lebesque measurable subset of the interval (O,1) and t is any irrational number in that interval, then by a well-known theorem of Weyl, the frequency with which the integer products of t modulo one fall in A converges to the measure of A. This result may be used to evaluate asymptotic error in certain approximations. For a special case, Weyl's theorem is shown to extend to rational numbers t and a lower bound on frequency is derived.
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THE DETERMINANTS OF EMERGENCY AND ELECTIVE ADMISSIONS TO HOSPITALS
June 1, 1974
This paper investigates three topics associated with admissions to non-profit, short-term hospitals. It examines properties of alternative models for predicting daily emergency hospital admissions, structures a cross-section time-series model of emergency admissions to individual hospitals, and formalizes and tests a descriptive model of hospital admissions decisions on urgent and elective patients.
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THE COVARIANCE MATRIX OF THE LIMITED INFORMATION ESTIMATOR AND THE IDENTIFICATION TEST - COMMENT
June 1, 1974
Comment on a proposed new estimator of the large sample asymptotic covariance matrix for the limited information maximum likelihood estimator in simultaneous equations.
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ESTIMATION OF MULTINOMIAL PROCESS WHEN ONLY THE SUM AND THE NUMBER GOVERNED BY EACH PROCESS IS OBSERVED
June 1, 1974
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.
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MARKOV Duels
June 1, 1974
This paper develops duel models for the situation in which the outcomes from a finite stationary Markov chain and both weapons have an unlimited supply of ammunition, fire at constant intervals of time, and duel until one is killed.
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TESTING A SUBSET OF THE OVERIDENTIFYING RESTRICTIONS
June 1, 1974
Tests a proposed likelihood ration statistic on a particular overidentified model.
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A DECOMPOSITION PROCEDURE FOR THE QUADRATIC ASSIGNMENT PROBLEM
June 1, 1974
This paper presents a decomposition procedure for reducing the running time of large quadratic assignment problems incorporating the N-step, 2-variable search algorithm. Running time reductions as well as improved solution values are demonstrated for the Steinberg test problem.
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AN APPROACH TO SEMI-MARKOV PROCESSES
June 1, 1974
This paper reports on some of the mathematical results that the author obtained while seeking to refine the Markov chain models used in air ASW tactical analyses in numerous studies done at CNA. In an effort to take into account the waiting time in each state prior to transition, a non-Markov process was postulated. Subsequent investigation showed the process to be a reformulation of a semi-Markov process.
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