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.
Highlights
Let 0 = U(0) ≤ U(1) ≤ U(2) ≤⋅⋅⋅≤ U(n−1) ≤ U(n) = 1 be the order statistics of a random sample of size (n-1) from the U(0,1) distribution
The main result of this paper is the following Theorem
We proved the weak convergence of a stochastic process defined in terms of partial sums of randomly weighted powers of uniform spacings
Summary
Let 0 = U(0) ≤ U(1) ≤ U(2) ≤⋅⋅⋅≤ U(n−1) ≤ U(n) = 1 be the order statistics of a random sample of size (n-1) from the U(0,1) distribution. Be arbitrary but fixed and assume that n=mk. The U (0,1) k-spacings are defined as. Be iidrv with E(Xi)=μ, Var(Xi)=ó2
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