ScienceAsia 28 (2002) :055-060 |doi: 10.2306/scienceasia1513-1874.2002.28.055

The Central Limit Theorems for Sums of Powers of Function of Independent Random Variables

K Laipaporn^a and K Neammanee^*,b

ABSTRACT: Let (X_nk), k = 1, ..., k_n ; n = 1, 2, ... be a double sequence of infinitesimal random variables which are rowwise independent. In this paper, we give necessary and sufficient conditions for the sequence of distribution functions of to weakly converge to a limiting distribution function F_r for each natural number r, and also for convergence of (F_r).

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a Department of Mathematics, Walailak University, Nakhon Sri Thammarat 80160, Thailand.
b Department of Mathematics, Chulalongkorn University, Bangkok 10330, Thailand.


* Corresponding author, E-mail: k_neammanee@hotmail.com

Received 22 Feb 2001, Accepted 11 Sep 2001