Explicit Projection Bounds for Spacings under DRFR Constraints

Accepted June 2026

Abstract

Let X₁,...,X_n be i.i.d. random variables with distribution function F. Assume that F succeeds a baseline distribution in the convex transform order. For a suitable Pareto-type baseline, this condition corresponds to the decreasing reversed failure rate (DRFR) property, to which we restrict attention. We derive sharp upper bounds for the standardized expectations of spacings over the DRFR class. We obtain explicit formulas for the relevant $L^2$-projections, describe the extremal distributions attaining the bounds, and provide a geometric interpretation of the extremal cases. Numerical illustrations are also included.