The paper concerns a situation in which there are M hypotheses H/sub 1/,. . ., H/sub M/, and in which Y is a random variable taking values in a set Y', with a different probability distribution under each hypothesis. A quantizer gamma :Y' to (1,. . ., D) is applied to form a quantized random variable gamma (Y). The extreme points of the set of possible probability distributions of gamma (Y) are characterized as gamma ranges over all quantizers. Optimality properties of likelihood-ratio quantizers are then established for a very broad class of quantization problems, including problems involving the maximization of a distance measure as discussed by S.M. Ali and S.D. Silvey(1966).
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机译：本文涉及其中有M假设H / SUB 1 /。 。 。H / sub m /，其中y是一个随机变量在集合Y'中取值，在每个假设下具有不同的概率分布。量化器γ：Y'至（1，。。。。。。。。。。。。。。。D）形成量化随机可变伽马（Y）。伽马（Y）的可能概率分布的一组极端点的特征在于所有量化器上的伽马范围。然后建立似然比量化器的最优性能，用于非常广泛的量化问题，包括涉及如下所讨论的距离测量的最大化的问题。阿里和S.D. SILVEY（1966）。
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