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. The Egyptian Statistical Journal, 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". The Egyptian Statistical Journal, 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', The Egyptian Statistical Journal, 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. The Egyptian Statistical Journal, 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
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
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