Sharp bounds for expectations of spacings from decreasing density and failure rate families
Volume 31 / 2004
Applicationes Mathematicae 31 (2004), 369-395
MSC: Primary 60E15, 62G30; Secondary 62N05.
DOI: 10.4064/am31-4-1
Abstract
We apply the method of projecting functions onto convex cones in Hilbert spaces to derive sharp upper bounds for the expectations of spacings from i.i.d. samples coming from restricted families of distributions. Two families are considered: distributions with decreasing density and with decreasing failure rate. We also characterize the distributions for which the bounds are attained.
