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VOL. 1 | 2018 Chapter 21. Strong limits related to the oscillation modulus of the empirical process based on the k-spacing process
Gane Samb LO

Editor(s) Hamet SEYDI, Gane Samb LO, Aboubakary DIAKHABY

## Abstract

Recently, several strong limit theorems for the oscillation moduli of the empirical process have been given in the iid-case. We show that, with very slight differences, those strong results are also obtained for some representation of the reduced empirical process based on the (nonoverlapping) k-spacings generated by a sequence of independent random variables (rv’s) uniformly distributed on $(0, 1)$. This yields weak limits for the mentioned process. Our study includes the case where the step $k$ is unbounded. The results are mainly derived from several properties concerning the increments of gamma functions with parameters $k$ and one.

## Information

Published: 1 January 2018
First available in Project Euclid: 26 September 2019

Digital Object Identifier: 10.16929/sbs/2018.100-04-04

Subjects:
Primary: 60B10, 60F15, 60G30

Rights: Copyright © 2018 The Statistics and Probability African Society

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