Bayes Estimation Of Normal Mathematical Expectation With Unilateral Interval Information

In the paper, we analyze an estimated problem of normal mathematical expectation with unilateral interval information been met in practical work of survey, Using Bayes statistic approach, we get Bayes estimation of normal mathematical expectation. In military practice, used the result of this paper, it proved that the Bayes result of this paper could reduce the systematic error of measure under less experiment times.This paper has six chapters, we give the summary as follows:In the first chapter, we introduce the knowledge of realistic background. Through introducing realistic background of the matter , preferring the matter, and analyzing the shortage of formers' results on the matter, we give out the work of the paper.In the second chapter, we explicate the theoretical knowledge, Bayes statistic approach, which be applied in the paper, we show the definition of the prior distribution and how to select the prior information, we show the relation of prior distribution, conditional distribution and posterior distribution, we also show statistical inference approach and the key of how to use Bayes statistic approach.In the third chapter, we introduce the correct theory knowledge.In the fourth chapter, to the first time sample error of measure z l,using Bayes statistic approach, we get Bayes estimation of the systematic error:f(z) is density function of N(0,02 + 2 ) which is boundary distribution of Z .After using the result of the first time measure to correct the systematic error, the second time sample error of measure also has z l, we can get Bayes estimation of the systematic error:f1(z) is density function of N(0, 12+ 2) which is boundarydistribution of Z, after having the results of two time measure.After using the result of the first time measure to correct the systematic error, but the second time sample error of measure has z -l, we can get Bayes estimation of the systematic error:In the fifth chapter, we use the result of this paper in military practice.