On a Non-parametric Test in Life Test

[2], [3], G. Ishii [5] . In a previous paper, we had treated the test of fit in life test in the case that we stop when the s-th death has occurred, G. Ishii [4] . In the present paper we treat the case when we stop the life test at a certain preassigned time T. Let X be a random variable having the continuous distribution function. In order to test the hypothesis Ho that the distribution function is a known function F(x), F. N. David [1] and M. Okamoto [6] have proposed the following non-parametric test : Let xi (i =1, 2, , M) be M independent observation of a random variable X. There are real numbers i =1, 2, , m— 1 such that F(a,) —F(at _i) —1/m, i = 1, 2, --, m where ao= — co, am= + (ai_i, ai] will be called " part." Let v be the number of parts which contain no x's. If v is too large, we reject Ho. Now we shall apply the above non-parametric test to life test.