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This paper applies the exponential distribution to stock price reactions to determine, at three confidence levels, the critical percentage price reaction beyond which a reaction constitutes a strong likelihood of a major reversal or halt in the stock's present general price trend. We show that these critical values can be used to determine stop losses, so that a trader's position is closed when the probability of a major reversal or halt against his position is large, and an open position is kept open when the probability that the reaction is a major one is small or moderate. The distribution fit on ten stocks on daily and weekly bases for over a year's duration each, tested using the chi-squared statistic, was found to be good. Further, three stops, corresponding to three confidence levels of the distribution were tested for each stock against a subsequent six-month period of price action. The percentage of successful tests of these stops for each of the stocks corresponded very closely to expected results ascertained by using data from the previous period. [ABSTRACT FROM AUTHOR]

This article is concerned with some problems that occur in certain tactical considerations: how should one place k circles [spheres] in the plane [3- space] so that their union has the greatest standard normal probability measure, that is, so as to maximize the probability that a random normal point will fall in one or more of the circles [spheres]. For k>3 the problem seems hopeless, (except for certain special situations); the case for k=3 is still unresolved and is being worked on by a number of investigators, and the case for k=2 is solved completely in this paper. The results for k=2 have some practical value when applied to actual problems arising in tactical considerations, and some theoretical value, as a method of attacking the problem for k≥3. [ABSTRACT FROM AUTHOR]

A method suitable for hand computation is presented for determining the probability of killing a point target when (a) the lethal volume is a sphere centered on the burst point of the weapon, and (b) the distribution of the weapon's burst points is described by a three-dimensional multivariate normal distribution about the target. [ABSTRACT FROM AUTHOR]