Accession Number : AD0784388

Title :   On Bounding Moments From Grouped Data for Unimodal Density Functions.

Descriptive Note : Technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS

Personal Author(s) : Krieger,Abba M.

Report Date : JUN 1974

Pagination or Media Count : 30

Abstract : This paper extends the work done in another paper. In that paper the author derived bounds for the integral h(x)dF(x) where h(x) 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 h(x)dF(x). 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)

Descriptors :   *Analysis of variance, *Distribution functions, Probability density functions, Normal density functions, Curve fitting, Theorems

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE