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This paper gives a description of how to find the 'best' sequence of allocation of resources to projects. The method handles simultaneously a great number of projects. The expression 'best' sequence means here the priority-rating that optimizes some chosen measure for the efficiency of the system. This optimization is done within the limits of the total resources available for allocation to projects. The problem is solved for whatever dependency there may be between resource quantity and system efficiency for the single projects. It works for the 'difficult' case of discontinuous efficiency functions as well. It is shown that in order to handle a great number of projects, one can divide the projects into groups, apply the method within each group of projects, then consider each group as a super project, and finally solve the whole problem by using the same method on groups. The problem is solved by a combination of the dynamic programming method, Lagrange's multiplier method, and numerical calculations on an electronic computer. The main part of the method is shown in a flow-diagram form. In the last sections of this paper practical examples are given, where the method is applied on investment problems. [ABSTRACT FROM AUTHOR]

This paper is written with three objectives in mind. First, to point out that the problem of grouping, where a larger number of elements n are combined into m mutually exclusive groups (m ~n) should be recognized as a problem in Integer Programming, and that such recognition can help us in avoiding complete enumeration of stages in grouping from n to n - 1 ... to m, and of alternative possibilities in each stage. Second, to formulate mathematically some simple versions of the relevant Integer Programming Problem, so that the available computer codes can solve it. When the grouping attempts to minimize the within groups sums of squares, the so-called string property is proved to be necessary for the minimum (Lemma 1). It is shown that the string property can be exploited to write the non-linear within group sums of squares as a linear function (Lemma 2). An attempt is made to generalize the string property for the higher dimensional case. Third, to give some numerical examples to clarify the mathematical models and to illustrate the advantages of Integer Programming formulation by comparing with the numerical examples appearing in the literature [8], [13 ]. Zero-one programming where the integer variables can take values of zero or one only appears to be most efficient from the limited experience of the author. The paper is divided into three sections which closely correspond to the three objectives noted above. [ABSTRACT FROM AUTHOR]

The paper is concerned with randomized experiments with one treatment. Two randomization schemes are considered: randomized pairs and unrestricted randomization. If effective at all, the treatment is supposed to affect the conditional distribution of the "experimental" variable Y given another variable X, called "predictor". The distribution of X is not affected by the treatment. Using the general theory published elsewhere, the paper deduces the locally asymptotically optimal test of the hypothesis that the treatment has no effect. Apart from the usual difficulties connected with asymptotic tests (how large must N be?), the theory is easily applicable in many "live" cases even though the conditional distribution of Y given X may contain nuisance parameters and be of unusual form. [ABSTRACT FROM AUTHOR]

This paper illustrates the simulation method of evaluating the effect of system component changes on highway crash reduction. The evaluation procedure presented uses operating characteristics of a component as input, and compares the performance of alternative components in emergency traffic conflict situations. It is shown that Monte Carlo simulation of the model may he an efficient technique for comparing component alternatives. The examples presented involve (1) the emergency braking capabilities of two populations of vehicles in emergency car-following situations, and (2) two different rear lighting systems. [ABSTRACT FROM AUTHOR]

Interprets the comments on a paper which modified the Bode-Titius law, a numerological law that gives an approximate formula for the mean distances of the planets from the Sun. Values of Bode-Titius distances; Impact of Bode's law on the hypothesis of a non-cataclysmic origin of the solar system. [ABSTRACT FROM AUTHOR]

In many situations, approximation of a set of data by a polygonal curve is more advantageous than approximation by a polynomial. If the join points of the polygonal curve are known, the problem is quite simple. If, however, they are to be chosen in some expeditious fashion, considerable numerical difficulties can arise if the curve-fitting problem is approached directly. In this paper it is shown that dynamic programming offers a simple direct approach to the determination of an optimal fit. [ABSTRACT FROM AUTHOR]

Let X[sub 1], ... , X[sub m] and Y[sub 1], ... , Y[sub n] be independent random samples from populations having continuous d.f.'s psi((x-micro)/sigma) and psi((y-nu)/tau) respectively. The classical F-test of a hypothesis concerning angle = tau/sigma is known to be non-robust. This paper examines several robust alternative procedures and compares them on the basis of Pitman a.r.e and Monte Carlo studies of power functions. An approximate permutation test [13] and a "jackknife" procedure [9] are found to be most satisfactory; while a class of "rank-like" tests [10] are found to be "useful inefficient statistics" [ABSTRACT FROM AUTHOR]

This paper deals with certain aspects of variance-component estimation for the unbalanced two-way completely-random classification where the numbers of observations in the subclasses are treated as random variables not necessarily independent of some of the random effects of the model. General results are given on the expectations of two commonly-used estimators of the vector of variance components. Numerical approximations are presented for these expectations for one sub-family of the family of all possible joint distributions of the subclass numbers and the random effects. [ABSTRACT FROM AUTHOR]

The numerous sources of variation among life tables are reducible to two. This paper finds expressions for these separately. The first source of variation is the rate of increase attributed to the observed population. A given underlying continuous curve of mortality by age will show somewhat different age-specific death rates according to the rate of increase of the population subject to the given mortality. At ages beyond about 15, for a given underlying mortality, the age-specific rates observed will be lower the more rapid the increase. Conversely, to infer the stationary age-specific rates from observed rates a larger quantity must be added the greater the increase to which the observed population is subject. The second source of difference is the form of the curve put through the (discrete) l[sub x], the number living to age x, to integrate and find [sub n]L[sub x], the number in the stationary population from age x to x + n. Some considerations are presented on the choice which must be made on each of these two matters, the life table being fully specified to the last decimal place once those choices are made. Finally, a recommended procedure for making life tables is provided, covering special devices for the early and terminal ages, using a new formula (6) which provides more rapid iteration for the ages from 5 to 80. [ABSTRACT FROM AUTHOR]

While distribution-free procedures are often appropriate when testing statistical hypotheses, they may become complicated or involve loss of power when the data are grouped. For rank tests the ties caused by grouping are generally broken either by using a randomization procedure or averaging the tied ranks. In this paper the power loss due to equi-spaced grouping (in terms of Pitman asymptotic relative efficiency) is investigated for some commonly used tests, for each method of tie-breaking. The tests considered are Wilcoxon's and Mood's tests for the two-sample problem, Mann's test for randomness, and Pitman's independence test. It is shown how the power loss depends on the width of the grouping intervals and the distribution of the data, and some numerical studies are given. The results seem to indicate that the power loss is small even for a sizable group interval, and that it may be preferable to break ties by randomization than by averaging ranks. [ABSTRACT FROM AUTHOR]

This paper presents in a form convenient for applications a number of bounds for distributions with monotone hazard rate. These bounds, together with their proofs and various generalizations have been obtained by Barlow and Marshall (1964). However, many of them can be characterized only through solutions of transcendental equations, and machine calculation has been necessary to make them accessible. Section 2 gives a listing of the results, and those without explicit forms are tabulated. Section 3 lists various related bounds which are of interest for purposes of comparison, and for use when the hypothesis of monotone hazard rate is not satisfied. Applications of the bounds are discussed in Section 4, together with some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper we obtain a multivariate generalization of the inverted beta distribution. Properties of this distribution and its connection with the multivariate Student-t distribution are discussed. Two asymptotic formulae for approximating the related probability integral are developed and illustrated with numerical examples. Application of this distribution to a problem in Bayesian inference is given. [ABSTRACT FROM AUTHOR]

In the classification of the elements in a binomial population, there is in many cases a chance of misclassifying an item. When an item in a sample from a binomial population is misclassified, it causes a bias, independent of the standard error, in the estimate of the population parameter P. This paper analyzes this bias when each of two interviewers independently classify the items in a single sample. Upper and lower bounds for the bias are derived. [ABSTRACT FROM AUTHOR]

This paper compares general and linear regression for the biextremal and Gumbel bivariate extreme models. The technique is based on the values of the correlation ratios and coefficients. The computations show that linear regression is a good approximation to the general one in both cases. [ABSTRACT FROM AUTHOR]