On the sum of ordered spacings

TL;DR

This paper derives the exact probability distributions for the sum of ordered spacings, including boundary cases, with potential applications across physical sciences and beyond.

Contribution

It provides analytic forms of the distributions for the sum of ordered spacings, covering boundary-included and excluded cases, with explicit densities and cumulative functions.

Findings

Analytic probability densities for sum of ordered spacings

Explicit cumulative distribution functions provided

Applicable to physical sciences and other fields

Abstract

We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability densities as well as their cumulatives are provided. These results will have useful applications in the physical sciences and possibly elsewhere.