Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An improvement of the Berry--Esseen inequality with applications to
  Poisson and mixed Poisson random sums   By a modification of the method that was applied in (Korolev and Shevtsova,
2009), here the inequalities
$$\rho(F_n,\Phi)\le\frac{0.335789(\beta^3+0.425)}{\sqrt{n}}$$ and
$$\rho(F_n,\Phi)\le \frac{0.3051(\beta^3+1)}{\sqrt{n}} $$ are proved for the
uniform distance $\rho(F_n,\Phi)$ between the standard normal distribution
function $\Phi$ and the distribution function $F_n$ of the normalized sum of an
arbitrary number $n\ge1$ of independent identically distributed random
variables with zero mean, unit variance and finite third absolute moment
$\beta^3$. The first of these inequalities sharpens the best known version of
the classical Berry--Esseen inequality since
$0.335789(\beta^3+0.425)\le0.335789(1+0.425)\beta^3<0.4785\beta^3$ by virtue of
the condition $\beta^3\ge1$, and 0.4785 is the best known upper estimate of the
absolute constant in the classical Berry--Esseen inequality. The second
inequality is applied to lowering the upper estimate of the absolute constant
in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051
which is strictly less than the least possible value of the absolute constant
in the classical Berry--Esseen inequality. As a corollary, the estimates of the
rate of convergence in limit theorems for compound mixed Poisson distributions
are refined.

37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas