Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete monotonicity of multinomial probabilities and its application
  to Bernstein estimators on the simplex   Let $d\in \mathbb{N}$ and let $\gamma_i\in [0,\infty)$, $x_i\in (0,1)$ be
such that $\sum_{i=1}^{d+1} \gamma_i = M\in (0,\infty)$ and $\sum_{i=1}^{d+1}
x_i = 1$. We prove that \begin{equation*} a \mapsto \frac{\Gamma(aM +
1)}{\prod_{i=1}^{d+1} \Gamma(a \gamma_i + 1)} \prod_{i=1}^{d+1} x_i^{a\gamma_i}
\end{equation*} is completely monotonic on $(0,\infty)$. This result
generalizes the one found by Alzer (2018) for binomial probabilities ($d=1$).
As a consequence of the log-convexity, we obtain some combinatorial
inequalities for multinomial coefficients. We also show how the main result can
be used to derive asymptotic formulas for quantities of interest in the context
of statistical density estimation based on Bernstein polynomials on the
$d$-dimensional simplex.

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The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th