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In some areas of life testing, subjects may enter or leave the study after they have been put on test. Statistics are presented for testing the hypothesis that the lifetimes have a given distribution for both the discrete and continuous cases. They are shown to be asymptotically normal by associating a martingale with the life process and using basic results about stopping times. There is some discussion of the effect of weight functions on power. An example of the test is provided.
James S. Hyde (Mon,) studied this question.