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Instruments and Systems: Monitoring, Control, and Diagnostics

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Testing of parametrical hypotheses at different supervision intervals of sampled values
S.V. Vlasova

The question about parameter assessment when part of the experimental data is beyond under control in the time interval T is considered
in the article. The suggested approach is based on the application of the technique of testing parametrical hypotheses. For this method,
however, it is necessary to identify the analytical form for distribution law of observed random variable. This task could be solved by using
conditional density function for sampled values, the condition for which will be the number of observed sampled values. The fact that the
maximum likelihood estimation in such cases can give less proper result than the offered approach is demonstrated in the paper.
The boundary of critical region at the process of accepting competing parametrical hypotheses using the Pirson theorem is defined by
the constant C, which could be chosen on the basis of variational principals with application of optimum criteria. Thus it allows us to take
into account the consequences of accepted decision, which can have different weighs (costs) of errors.
Keywords: parametrical hypothesis, parameter assessment, optimum criterion for splitting sampled area, functional, variation of functional.

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