Evaluating Improvements for Spacings of Order Statistics

We evaluate sharp upper bounds for the consecutive spacings of order statistics from an i.i.d. sample, measured in scale units generated by various central absolute moments of the parent distribution. The bounds are based on the projection method combined with the Hölder inequalities. We characterize the probability distributions for which the bounds are attained. We also evaluate the so obtained bounds numerically and compare them with other existing bounds.