A Spacing Estimator

TL;DR

This paper introduces a new spacing estimator applicable to distributions with known inverse CDFs, extending previous work to logistic and Gumbel variates, with high accuracy in the middle but reduced performance in the tails.

Contribution

It extends the known distribution of spacings to logistic and Gumbel variates and proposes an estimator for these cases, improving understanding of order statistic differences.

Findings

Estimator is highly accurate near the middle of the distribution.

Performance degrades by up to 20% in the tails.

Extends known spacing distribution to new variates.

Abstract

The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a known inverse cumulative density function. We show the estimator is accurate to the limit of numerical simulations for points near the middle of the order statistics, but degrades by up to 20% in the tails.