On the Uniform Rates of Convergence in the Central Limit Theorem for Functions of the Average of I. I. D. Random Variables
Kirkire (Baroda), P. (1993). On the Uniform Rates of Convergence in the Central Limit Theorem for Functions of the Average of I. I. D. Random Variables. EKB Journal Management System, 37(1), 59-64. doi: 10.21608/esju.1993.314834
Prashant Kirkire (Baroda). "On the Uniform Rates of Convergence in the Central Limit Theorem for Functions of the Average of I. I. D. Random Variables". EKB Journal Management System, 37, 1, 1993, 59-64. doi: 10.21608/esju.1993.314834
Kirkire (Baroda), P. (1993). 'On the Uniform Rates of Convergence in the Central Limit Theorem for Functions of the Average of I. I. D. Random Variables', EKB Journal Management System, 37(1), pp. 59-64. doi: 10.21608/esju.1993.314834
Kirkire (Baroda), P. On the Uniform Rates of Convergence in the Central Limit Theorem for Functions of the Average of I. I. D. Random Variables. EKB Journal Management System, 1993; 37(1): 59-64. doi: 10.21608/esju.1993.314834

On the Uniform Rates of Convergence in the Central Limit Theorem for Functions of the Average of I. I. D. Random Variables

The Egyptian Statistical Journal
Article 6, Volume 37, Issue 1, June 1993, Page 59-64  XML
Document Type: Original Article
DOI: 10.21608/esju.1993.314834
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Author
Prashant Kirkire (Baroda)
Abstract
Let {Xk, k => 1} be a sequence of i.i.d.r.v.s with common distribution function (d.f.) F. Suppose F belongs to the domain of normal attraction of a stable law  with index σ, 1 < σ  ≤ 2 and F satisfies some regularity conditions. Let Sn = X1 + ... + Xn  and g be a real differentiable function such that |g'(x) - g'(y)| ≤ L |x - y|, L>0. We give uniform rate of convergence in the Central Limit Theorem (CLT) for the sequence:
( (n^1-r) / g'(o) ) { g(sn / n) - g(0) },  n ≥ 1, g'(0) ≠ 0
Keywords
Central Limit Theorem; Differentiable Function; Regularity Conditions; Uniform Rates of Convergence
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