RESEARCH ARTICLE
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
Article Information
Identifiers and Pagination:
Year: 2020Volume: 10
First Page: 1
Last Page: 7
Publisher Id: TOSPJ-10-1
DOI: 10.2174/1876527002010010001
Article History:
Received Date: 02/02/2019Revision Received Date: 06/11/2019
Acceptance Date: 16/11/2019
Electronic publication date: 14/02/2020
Collection year: 2020
© 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: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract
Objectives:
To study the asymptotic theory of the randomly wieghted partial sum process of powers of k-spacings from the uniform distribution.
Methods:
Earlier results on the distribution of the uniform incremental randomly weighted sums.
Methods:
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.
