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
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
MLA
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
HARVARD
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
VANCOUVER
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
)
View on SCiNiTO