The Open Mathematics, Statistics and Probability Journal

2020, 10 : 1-7
Published online 2020 February 14. DOI: 10.2174/1876527002010010001
Publisher ID: TOSPJ-10-1

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

Emad-Eldin A. A. Aly1, *

*Address correspondence to this author at Department of Statistics & Operations Research Faculty of Science, Kuwait University, Safat 13060, Kuwait; Tel: +965 66655671; E-mail: eealy50@gmail.com

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.