Incomplete Data Index Under The Overall Parameter Estimation

In the daily statistical work, data collection is indispensable. But due to some reasons, people may see many kinds of missing data in the actual work. Such as the artificial damage of testing samples, or the disconnection with the respondents, and so on. Because of this, we will gain samples with missing data (or called incomplete data). Usually we do not deal with these samples with the common ways. This is because If we do, the samples containing missing data will lead us to so large residuals that the estimations would turn to be useless. In this case, people should use special methods to handle those incomplete data. This article was aimed to analysis missing data from some models that was already known, and then study the methods to deal with them properly. First, the article discussed a model called Two Exponential Populations with missing data. Then, the EM algorithm of Mixed Two-parameters Exponential Distribution with incomplete data under the normal stress life time test.The structure of article is as follows:Chapter1is Introduction. In this chapter, the background of statistical researches on missing data was generally introduced, and the specific structure of this article was given too.Chapter2is the theoretical basis. All the concept, statistical methods, and statistical properties are introduced in this chapter.Chapter3is one of the key points in this article. The MLE and the test for the parameters of two exponential populations both with missing data are discussed in this chapter. The strong consistency of and asymptotic normality of estimators are both proved. Then the test of hypothesis of the populations and the asymptotic confidence interval of the difference between two parameters are also given based on the limit distribution discussed in this paper.Chapter4is the other key point. In this chapter, we employ the EM algorithm to obtain the MLE for the mixed Two-parameters Exponential Distribution model under the normal stress life time test with full data or censored samples. The estimation formulas are also given in this chapter. Chapter5is the conclusion and foresight.