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Assignment problems arise whenever elements of a finite set have to be paired with elements of another finite set in such a way as to maximize a certain function of the pairing. In this paper three different formulations of such a problem are given. They are analyzed and a method for obtaining a low-cost solution is developed. [ABSTRACT FROM AUTHOR]

A point target is randomly located according to an offset circular normal distribution arid remains in its unknown position throughout N independent tosses of a lethal circle. The paper presents integral expressions for the probability of: (1) killing the target at least once in N tosses of the lethal circle; (2) killing the target exactly it times in N tosses; (3) requiring less than or equal to m shots to kill the target exactly once; (4) killing the target at least once in N tosses when the bias (offset distance) is randomly distributed. The paper also presents formulas for the expected number of shots required to kill the target exactly once and the expected number of times the target is killed in N tosses. A simple expression is also given for the single-shot kill probability for an offset ellipsoidal case when the lethal radius of the weapon is variable rather than fixed. [ABSTRACT FROM AUTHOR]

This paper studies a particular random tour (continuous random walk): A particle moves in two dimensions at constant speed by choosing successive travel directions that are independent and uniformly distributed between 0 and 2π, with the lengths of the steps between direction changes being independent, exponentially distributed, random variables. An analytic expression for the probability density of the particle's position after a time t is derived, and an application is made to a military situation where the 'particle' is a target trying to escape being destroyed by an unseen enemy. The bulk of the paper is devoted to deriving the density function. [ABSTRACT FROM AUTHOR]

This article presents information on slanted subjective probabilities and randomization. The randomization argument contains a concession to the frequentist-objectivist school in probability theory. This is because the argument recognizes that reasonable individuals may be reluctant to base their actions on unstable and controversial degrees of belief, except if it can be specifically demonstrated to them that in the given circumstances these beliefs are equivalent to the stable and uncontroversial beliefs which they have concerning practically fair coins or dice, well-shuffled cards, etc. The repetitive processes generated by practically fair devices of the latter type are the "standard processes" of the author's symposium paper: they all are well-behaved processes by frequentist-objectivist criteria. When a subjectivist develops a randomization argument he makes the concession of attributing special significance to standard-process probabilities. The author's own position too is subjectivistic but he too favors some degree of hybridity.

In the present paper a two-server queuing process fed by Poisson arrivals and exponential service time distributions has been considered under the bulk-service discipline. Time-dependent probabilities for the queue length have been obtained in terms of Laplace transforms, from which different measures associated with the queuing process could be deter- mined. The mean queue-length and the distributions of the length of busy periods for (1) at least one channel is busy and (ii) both channels being busy, are obtained. [ABSTRACT FROM AUTHOR]

In 1965 Stanley Warner [8] illustrated a technique whereby one could estimate from a sample the proportion of persons in a population possessing some characteristic X, without pointedly asking the question, "Do you possess characteristic X?". The present article uses a variation of these ideas suggested by Warner in a later paper [7] to estimate the distribution function of a continuous-type random variable. The technique is illustrated by estimating an income distribution from the responses of a sample of 500 individuals. The potential use of devices of this type in maintaining confidentiality of existing data files is apparent. [ABSTRACT FROM AUTHOR]

This paper discusses the application of Bayes's theorem to those cases where the true state of the world is not known with certainty. An algorithm is proposed that relaxes the requirement of Bayes's theorem that the true data state be known with certainty by postulating a true but unobservable elementary event, ω, which gives rise to posterior probabilities which reflect the uncertainty of the data. A derivation is presented for the calculation of Bayesian posterior probabilities which uses as its input these probabilities, rather than the true event, o, which is assumed to be unavailable. Suggestions are made as to the application of this modification of Bayes's theorem to cascaded inference processes. [ABSTRACT FROM AUTHOR]

Provides information on a research about the paradox of voting. Potential effect of group decision processes based on a principle of majority rule on the rankings among alternatives; Implications of such paradox for the construction of social welfare functions; Cases for the distribution of probabilities over rankings among alternatives.

This article offers information on published literature on the class of coverage mathematical problems in industrial operations which appeared in the journal "Operations Research." While there is no single source to which the reader can turn for a comprehensive classification of the many variations and special cases of the coverage problem, there are two less comprehensive sources that have come to the editor's attention that should be of use in placing new developments in context and in locating techniques and mathematical tables for specific applications. The first source is an article by William C. Guenther and Paul J. Terragno titled "A Review of the Literature on a Class of Coverage Problems," which was published in the 1964 issue of the journal "Annals of Mathematical Statistics." This article considers the multidimensional single-shot kill probability of a weapon against a point target when the impact point of the weapon, the position of the target, and the damage function are given arbitrary probability distributions. The second source is a bibliography titled "The Coverage Problem," issued as Sandia Corporation Report SCR-443.

This note deals with two studies. The first considers an estimate of the probability of being within a given radius. The minimum variance unbiased estimates is derived in this case. The second study considers the estimate of the circular probable error wherein an order statistic estimate is used. [ABSTRACT FROM AUTHOR]

The Kuhn-Tucker necessary conditions for a local maximum of a differentiable function subject to differentiable inequality constraints, are derived by showing that the classical necessary conditions for a local maximum of a differentiable function of N variables subject to less than N equality constraints, are also meaningful when there are N or more equality constraints, if appropriate assumptions, similar to Kuhn and Tucker's `constraint qualification,' are made. [ABSTRACT FROM AUTHOR]

The article deliberates on why sociological knowledge is not cumulative. Scientific knowledge consists of a combination of empirical and theoretical knowledge. The former is the result of research or the collection of sense data, while the latter is concerned with the mental relations of non-observable constructs. Empirical knowledge cannot be added up to reach the level of theoretical knowledge if they are cognitively different. Facts do not add up to constructs or establish relations between them. Facts get their meaning from the powers of observation, but constructs get their meaning from their mentally established relations to each other. Relations between constructs, however, may be used to explain observed relations between facts. Cumulation, therefore, has a different meaning for each of the two types of knowledge necessary for the development of science. If the truth of theoretical generalizations cannot be established by induction, perhaps they can be constructed to be formally true, i.e., true by definition. The more general theoretical generalization is analytic while the less general empirical generalization is synthetic, meaning that no deduction can be made.

A stochastic model of adaptive behavior in a dynamic situation is proposed, and its properties developed. The model is developed from a hypothetical construct of behavior, and, in the limit, becomes a nonstationary probability diffusion process. Although the model has wide potential applicability, it is discussed in the marketing context for which the model was first proposed. In addition to properties of the model, important aspects of the model as it applies to marketing will be discussed. [ABSTRACT FROM AUTHOR]

Analyzing time series data for evidence of changes in market conditions is a problem central to development of a marketing information system. Examples are tracking field reports on competitors' prices and analyzing market share estimates computed from retail audits and consumer panel reports. These series may involve substantial random measurement error, and any changes, often small relative to this error, are difficult to detect promptly and accurately. One way to approach this problem is with techniques recently developed for handling time series with small stochastic mean shifts as well as random error. Two special procedures are compared in Monte Carlo analyses with a simpler data filtering and control-chart approach; the latter appears the most promising. [ABSTRACT FROM AUTHOR]

A system is observed periodically and classified into one of a finite number of states. On the basis of the observations certain maintenance or replacement decisions are made. Transitions probabilities from state to state are determined by the decisions. The problem considered is that of finding the decision rule which maximizes the expected length of time between replacements subject to the side conditions that the probabilities of replacement through certain undesirable states are bounded by prescribed numbers. [ABSTRACT FROM AUTHOR]

The optimal composition of cattle feed, which can be formulated as a linear programming problem in the case of certainty, is considered when compositions of inputs vary. In the corresponding linear programming formulation the coefficients of the constraints are not constant but can be considered as stochastic. Reformulating the constraints as chance constraints, a nonlinear programming problem results. For an illustrative example this problem is solved using one of Zoutendijk's methods of feasible directions. [ABSTRACT FROM AUTHOR]

The article focuses on the factors that are considered in the development and creation of criteria such as relevancy, reliability, and measurement combination. It states that among the three factors, relevancy was believed to emphasize on its judgmental nature and was considered as validity of the criterion. It says that realibility factor was considered based on its relationship with validity, sources of unrealibility, and false reliability. Meanwhile, combination of measures were discussed through the use of scale unit equality and sub-criteria weight.

Elementary probability statements are employed in causal inference models as an alternative to Blalock's correlation technique. By making use of certain simplifying assumptions, surplus equations become available for predictive use. Probability statements and predictions are shown for one-way causal models with causal chain, possibly spurious, and convergent patterns of relations. Fictitious data are used to illustrate the feasibility of probability models. Probability models thus provide another perspective for the kinds of causal models considered by Blalock. [ABSTRACT FROM AUTHOR]