部分範囲間の比について

In recent years the statistic relating to range have been used as the test functions on estimaters for the theories of the statistical inference. Especially in the processes of mass production, they are indispensable for simplicity and rapidity of computation in spite of less efficiency. In [1], [2] Dixon proposed the use of the ratio involving extreme values to test the outlying observation in normal type. On the whole the rejection tests in normal type have been investigated by many research workers, and good results have been realized. On the other hand in exponential type it was only M. Matsuyama in [3] who argued by making use of x^2-distribution. This paper investigates the properties of the statistic which have suggested by Dixon as test functions ahd here in paticular the statistic coming from exponential distribution are treated in detail.