38 citations · 121 across the 45 of their papers we have counts for
6 papers · 1 filter
Characteristic function of the positive part of a random variable and related results, with applications
Iosif Pinelis
Let be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) . Integral expressions for the c.f.\ of the r.v.'s in terms of $f…
Exact Rosenthal-type bounds
Iosif Pinelis
It is shown that, for any given , and , the exact upper bound on over all independent zero-mean random variables (r.v.'s) $X_1,\ldots,X_n…
Exact Rosenthal-type inequalities for p=3, and related results
Iosif Pinelis
An exact Rosenthal-type inequality for the third absolute moments is given, as well as a number of related results. Such results are useful in applications to Berry--Esseen bounds.
More on the nonuniform Berry--Esseen bound
Iosif Pinelis
Certain smoothing inequalities were proposed in the recent paper posted on arXiv at arxiv:1301.2828 in order to lessen the very large gap between the best correctly established upp…
An optimal bound on the quantiles of a certain kind of distributions
Iosif Pinelis
An optimal bound on the quantiles of a certain kind of distributions is given. Such a bound is used in applications to Berry--Esseen-type bounds for nonlinear statistics.
On the nonuniform Berry--Esseen bound
Iosif Pinelis
Due to the effort of a number of authors, the value c_u of the absolute constant factor in the uniform Berry--Esseen (BE) bound for sums of independent random variables has been gr…