On Reliability Hypothesis Testing for Continuous Object with Quantization

The problem of logarithmically asymptotically optimal hypothesis testing for a continuous random variable (CRV) is considered.It is assumed that M continuous probability distributions (CPDs) are known, and the object described by the CRV follows one of them.This problem, in the case of discrete probability distributions, was introduced and extensively studied in [1].In this paper, a quantization method is applied to continuous distributions.Some known results are generalized and reformulated for the continuous case.