A nonnegative martingale with initial value equal to one measures evidence against a
probabilistic hypothesis. The inverse of its value at some stop** time can be interpreted as …

It is shown that the absolute constant in the Berry–Esseen inequality for iid Bernoulli random
variables is strictly less than the Esseen constant, if $1\le n\le 500000$, where n is a number …

New bounds for the kk th-order derivatives of the solutions of the normal and multivariate
normal Stein equations are obtained. Our general order bounds involve fewer derivatives of …

In this short note, we prove an asymptotic expansion for the ratio of the Dirichlet density to
the multivariate normal density with the same mean and covariance matrix. The expansion is …

Abstract The Berry-Esseen theorem belongs to the classical theorems of probability theory.
The present work considers the case of X, X1,..., Xn independent and identically distributed …

The Kolmogorov distances between a symmetric hypergeometric law with standard
deviation $\sigma $ and its usual normal approximations are computed and shown to be …

Bounds for the error of the Gaussian approximation for the binomial distribution are stated,
depending from the probability of success and the number of observations. As a …

We prove a Berry-Esseen type inequality for approximating expectations of sufficiently
smooth functions $ f $, like $ f=|\cdot|^ 3$, with respect to standardized convolutions of laws …

В статье изложена история поиска безусловных и условных верхних оценок
абсолютной постоянной в неравенстве Берри–Эссеена для сумм независимых …

This thesis explores local and global normal and Edgeworth approximations for symmetric
binomial distributions. Further, it examines the normal approximation of convolution powers …