On Bounding Moments From Grouped Data for Unimodal Density Functions.
HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS
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This paper extends the work done in another paper. In that paper the author derived bounds for the integral hxdFx where hx is any convex function, the distribution function is concave and its values at several points are known, and the group means are given as well. A description is given of the two distribution functions which bound the integral hxdFx. These distributions are then used in obtaining bounds on the variance and Gini index for two examples. The number of groups in these examples is then changed in order to gain some feeling for the effect of the number of groups on the bounds. These results are extended in this paper to the case where the underlying density function is unimodal rather than decreasing. Author
- Statistics and Probability