Extreme distributions on intervals
One of the main tasks of interval computation is to analyze situations in which we only know the lower and upper bounds on the desired quantity, i.e., we only know an interval that contains this quantity. One of the objectives of such analysis is to make decisions. According to decision theory, a consistent decision making procedure is equivalent to assigning probabilities to different values within each interval. Thus, we arrive at the problem of describing a natural probability distribution on an interval. In this paper, we describe such a distribution for the practically important case of the "weakest link" arrangement, when the collapse of each link is catastrophic for a system. This situation occurs in fracture mechanics, when a fracture in one of the areas makes the whole plane inoperable, in economics, when the collapse of one large bank or one country can have catastrophic consequences, etc.