Interval Spacing
arXiv:2601.22116
Abstract
We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is equivalent to running a rectangular low-pass filter over the spacing, which simplifies the expressions for the expected values and introduces correlations between overlapping intervals.
19 pages, 5 figures ; v1 - added arXiv numbers to references