Interval Spacing

TL;DR

This paper introduces the concept of interval spacing, deriving its statistical properties for various distributions and linking it to low-pass filtering, providing new insights into data analysis techniques.

Contribution

It defines interval spacing, derives its density, mean, and variance for several distributions, and connects it to low-pass filtering, offering novel analytical tools.

Findings

Derived density, mean, and variance for uniform, exponential, and logistic distributions.

Established the equivalence of interval spacing to low-pass filtering.

Highlighted correlations between overlapping intervals.

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.