Periodic transformations of the sample average reciprocal value

Petr Lachout

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Upper bounds for minimal distances in the central limit theorem

Emmanuel Rio (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We obtain upper bounds for minimal metrics in the central limit theorem for sequences of independent real-valued random variables.

Comparing the distributions of sums of independent random vectors

Evgueni I. Gordienko (2005)

Kybernetika

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Let $(X_{n}, n \geq 1), ({\tilde{X}}_{n}, n \geq 1)$ be two sequences of i.i.d. random vectors with values in $ℝ^{k}$ and $S_{n} = X_{1} + \dots + X_{n}$ , ${\tilde{S}}_{n} = {\tilde{X}}_{1} + \dots + {\tilde{X}}_{n}$ , $n \geq 1$ . Assuming that $E X_{1} = E {\tilde{X}}_{1}$ , $E | X_{1} |^{2} < \infty$ , $E | {\tilde{X}}_{1} |^{k + 2} < \infty$ and the existence of a density of ${\tilde{X}}_{1}$ satisfying the certain conditions we prove the following inequalities: $v (S_{n}, {\tilde{S}}_{n}) \leq c max {v (X_{1}, {\tilde{X}}_{1}), ζ_{2} (X_{1}, {\tilde{X}}_{1})}, n = 1, 2, \dots,$ where $v$ and $ζ_{2}$ are the total variation and Zolotarev’s metrics, respectively.

On properties of binary random numbers

Jan Ámos Víšek (1974)

Aplikace matematiky

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Estimates of the rate of approximation in a de-poissonization lemma

Andrei Yu. Zaitsev (2002)

Annales de l'I.H.P. Probabilités et statistiques

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