Testing composite parametrical hypotheses without applying the reduction

9th International Conference on Modern Techniques of Plasma Diagnostics and their Application

Vlasov, V.^1 ; Vlasova, S.^2 ; Tolokonsky, A.^1

National Research Nuclear University MEPhI (MEPhI), Kashirskoe shosse 31, Moscow

115409, Russia^1

All-Russian Research Institute for Nuclear Power Plants, Ferganskaya st., 25, Moscow

109507, Russia^2

关键词: Composite hypothesis;    Distribution law;    Distribution parameters;    Exponential distributions;    Partition boundary;    Reduction method;    Stationary process;    Technological process;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/666/1/012034/pdf
DOI  :  10.1088/1742-6596/666/1/012034

来源: IOP

【 摘 要 】

Usually when the parametrical hypotheses are being tested the Wald reduction from composite hypothesis to the simple one is used. However, in order to apply the reduction method it is needed to know the distribution law of unknown parameter. Practically such a law cannot be determined precisely using the experimental data. First of all, it requires long supervision over the controlled stationary process to provide an inalterability of probability characteristics of the process. In practice the modifications in technological process could be made, and therefore the probability characteristics of the process can also change. Using the example of exponential distribution the algorithm of testing composite parametrical hypothesis about the distribution parameter which does not exceed the declared threshold value without use of reduction is considered in article. Such approach is based on the fact that the partition boundary of the sample space depends monotonously on unknown value of the interest parameter.