Abstract
Theorems of large deviations, both in the Cramer zone and the Linnik power zones, for the normal approximation of the distribution density function of normalized sum Sv = \sum∞ k=0 vkXk, 0 < v < 1, of i.i.d. random variables (r.v.) X0, X1, . . . satisfying the generalized Bernstein’s condition are obtained.
Highlights
Let X0, X1, . . . be a sequence of independent r.v. with the common distribution function F (x), and let v, 0 < v < 1, be a discount factor
The distribution Fv(x) of random variable Zv has been approximated by normal law Nv(x) and the exact estimate has been derived by H.U
The authors of the current paper proved in [ 2 ] the theorems of large deviations
Summary
Let X0, X1, . . . be a sequence of independent r.v. with the common distribution function F (x), and let v, 0 < v < 1, be a discount factor. Satisfying the generalized Bernstein’s condition are obtained. Be a sequence of independent r.v. with the common distribution function F (x), and let v, 0 < v < 1, be a discount factor.
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