A Spacing Estimator

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.

💡 Research Summary

This paper, titled “A Spacing Estimator,” makes significant contributions to the theory of spacings between consecutive order statistics. The author begins by noting that the exact distribution of spacings is only known for uniform and exponential random variates. The primary theoretical advancements of this work are the derivation of new analytical results for the expected spacing and its variance for two additional distributions: the logistic and the Gumbel (Extreme Value Type-I) distributions.

For the logistic distribution, the paper presents closed-form, albeit complex, series expressions for both the expected value E