| Abstract: | Abstract A one-dimensional random variable X is given. We have L points, µ1, µ2, …, µ L , and define the random variable Z = minµ h | X — µ h |, that is the distance to the nearest of the L points µ1, …, µ L . We want to find that set of points µ h for which the function  has a minimum. As we shall see in section 2, this problem is equivalent to finding L strata with the set of points of stratification x 1, x 2, …, x L?1 that makes  a minimum. wh is the probability mass and σ2 h the variance of the hth stratum. By differentiation of φ with respect to xh one can show 3] that a necessary condition for minimum is  where µh is the mean of the hth stratum. In section 2 we obtain this condition in another way, which at the same time gives a method of finding the points µh and xh . |
