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Let X1,X2, . . . ,Xn be independent and identically distributed random variables. We present an analytic method for computing the moments of Sn = Pn i=1 Xi. The method is illustrated with a simple...
In this work, we deal with approximations for distribution functions of non-negative random variables. More specifically, we construct continuous approximants using an acceleration technique over a w...
Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the...
Exact lower bounds on the exponential moments of min(y,X) and X I {X < y} are provided given the first two moments of a random variable X. These bounds are useful in work on large deviations probabi...
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically dis- tributed random variables converges weakly to a non-Gaussian ...
This note gives the convergence rate in the central limit theorem and the random central limit theorem of some functions of the average of independent random variables.
On the limit behaviour of random sums of independent random variables
Notions of independence for random variables
Conditioned limit theorems for functions of the average of i.i.d. random variables
Weak convergence of random sums of infima of independent random variables
Convergence rates in the strong law of large numbers for sums of random variables with multidimensional indices
We give tbe rate of convergence in the central limit theorem and the random central limit theorem for functions belonging to the class I of all real differentiable functions g such that gr E L(1).
Probabilities of moderate deviations for randomly indexed sums of independent and identically dmtributed random variables with multidimensional indices are studied. The results presented extend som...
The Levy and the Dudley metrics are used to give estimates of the rate convergence in the centrat- limit theorem for some functions of the average of independent random variables.

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