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, Pages 59-64 | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1993.314834 | ||
| 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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