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This paper gives analytic expressions for the distribution function of t", a doubly noncentral t-distribution, with nu degrees of freedom and noncentrality parameters delta and lambda, in series of Incomplete Beta and Hypergeometric (Gauss and Confluent) functions. Numerical values of Pr(t" ≤ t|v, δ, λ) for v = 2 (1) 20, λ = 0 (2) 8, |δ| = 0 (1) 5, t=0 and 1 are given in Table I. [ABSTRACT FROM AUTHOR]

This paper derives the simple analytic solution to the special but important inventory problem in which the optimal policy is to reorder whenever units are demanded. The demand distribution can be any compound Poisson; the resupply distribution is arbitrary. Both the backorder case and the lost sales case are solved by generalizing a queueing theorem due to Palm. The steady state probabilities for the number of units in resupply (or repair) completely describe the item's long term behavior, and are simply the normalized values of the compound Poisson demand distribution based on the mean of the resupply distribution but not on the distribution itself. Knowledge of these state probabilities enables us to compute several measures of item supply performance as a function of the spare stock, s. Traditional inventory analysis can then be applied to minimize total cost based on estimates of holding cost and supply performance cost. The appendices contain a description of the algorithm and the computer program for calculating stuttering Poisson state probabilities and the measures of effectiveness for the backorder case. Numerical illustrations are also provided. [ABSTRACT FROM AUTHOR]

Two characteristics of MCPL research efforts relating to the manipulation of cue redundancy are noted. First, the fairly prevalent problem of experimental confounding of cue redundancy with other task parameters, and second, the lack of an analytical development of the mathematical relationships among cue validities, task predictability, and regression weights as cue redundancy is varied systematically. This paper provides such an analysis, and shows that some of the confounding experienced by earlier researchers may be obviated. [ABSTRACT FROM AUTHOR]

The article focuses on empirical meaning in economics. For some time now, it has been the prevalent view of economists that universal, nonanalytic statements can be formulated in economics, which can be shown to be refutable, in principle, by reference to empirical data, and such statements typically express propositions concerning the signs of rates of change of "endogenous" variables with respect to "exogenous" variables. The economist's practice is characterized by the construction of taxonomic models which, when anchored to some particular space-time segment and thus become descriptions of that segment, may be tested by reference to data drawn from that segment. If tested and confirmed, they constitute an explanation. If untested, they constitute a prediction. Furthermore, the proposed structure for a particular space-time segment is selected, as it were, from a card file of structures on the basis of observations on that segment. Since the argument is rather involved, the author intends to make some necessary simplifications. Thus no distinction will be made between qualitative and quantitative economics or between static and dynamic structures or models.