Abstract
In the article, we research nonlinear estimations of a mathematical expectation of a random value received by the criterion of the minimum amount of deflections in a production degree that determinates a deviation weight. The research results can be used for the estimation of a mathematical expectation and determination of effectiveness of estimating in an information-measuring system based on light shields.
Highlights
In different information-measuring systems, including an information-measuring system based on light shields [1, 2] characteristics of random values according to independent samples are important
At the same time the approximate evaluation y according to MLM, received with the help of the function Minner at an initial estimate, equal to a mathematical expectation is more effective (e < 1, Table 1)
Approximate evaluations are more effective, and they can be used in the case of checking of statistical hypotheses when a mathematical expectation is supposed known
Summary
In different information-measuring systems, including an information-measuring system based on light shields [1, 2] characteristics of random values according to independent samples are important. One of these characteristics is a mathematical expectation. In this case, evaluations for point and interval estimation of for the control of statistical hypotheses are searched [3,4,5]. In a case of a point and interval estimation the criterion of valuation optimality (statistics y(x , ..., x ) – the function of sample values x , ..., x that does not depend on sample volume n) is minimum of its dispersion σ. It is obvious that the smaller a total risk is, the sharper an integral function of evaluation distribution F(y) is [5, 6]
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