The Single Is Normal Population Parameters At The Same Time The Local Inspection

Hitherto,on the statistic inference of multi-parameter from a population considered simultaneously, nobody hasn't begun to discuss it. As far as this problem is concerned,this paper will give a solution. And two important parameters(mean and variance) are considered simultaneously.that is to say, from the point of view of a test,this article tests simultaneously two parameters of one normal population. A test is put forward in the course of searching for α-UMPT making use of N-P lemma, and this paper has proved two things: one is that the level of the test is a, the other is the discussion about existence of the uniformly most powerful test.Then it shows a range that make our test . At last,the comparison has been made between its power and the power of the likelihood ratio test by simulation, and the exciting result explains that our test is more practicable, since the likelihood ratio test is only an approximate test.