Interval Spacing
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.
Fields of Study & Subjects
Probability and Statistical Research
Statistical Distribution Estimation and Applications
Point processes and geometric inequalities
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 29 January 2026
- Document type
- Preprint