On The Distribution of Partial Sums of Randomly Weighted Powers of Uniform Spacings

Emad-Eldin A. A. Aly1, *
1 Department of Statistics & Operations Research, Faculty of Science, Kuwait University, Safat 13060, Kuwait

© 2020 Emad-Eldin A. A. Aly.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at Department of Statistics & Operations Research Faculty of Science, Kuwait University, Safat 13060, Kuwait;
Tel: +965 66655671; E-mail:



To study the asymptotic theory of the randomly wieghted partial sum process of powers of k-spacings from the uniform distribution.


Earlier results on the distribution of the uniform incremental randomly weighted sums.


Based on theorems on weak and strong approximations of partial sum processes.

Results and conculsions:

Our main contribution is to prove the weak convergence of weighted sum of powers of uniform spacings.

Keywords: Uniform spacings, Weak convergence, Gaussian process, Incremental asymptotic convergence, Random Sample, k spacings.