Bombing Problems—A Statistical Approach

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Abstract
Bombing problems are studied from the viewpoint of statistical inference and from the viewpoints of the bomber and its opponent. The probability of a hit inside a circle centered at the target is given. A method is proposed to obtain the “best” estimate of the probability of a hit in a given area, with a known or unknown target, on the basis of the information given by the points of impact during a flight. The method is applied to the cases of a rectangle and of a circle centered at the (known) target. Methods of approximation for any area are given. The problem of “dangerous” and “safe” regions is discussed. A method to obtain “distribution free” safe regions is proposed and conditions to obtain “safe” regions with a given confidence level are stated. Two examples of “safe confidence regions” are given.

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