# LXX International conference "NUCLEUS – 2020. Nuclear physics and elementary particle physics. Nuclear physics technologies"

Oct 11 – 17, 2020
Online
Europe/Moscow timezone

## METHOD OF ANALYSIS OF LARGE ARRAYS OF DISCRETE EMPIRICAL DISTRIBUTIONS OF COUNTS WITH A SMALL SAMPLE NUMBER

Oct 16, 2020, 6:00 PM
25m
Online

#### Online

Oral report Section 3. Modern nuclear physics methods and technologies.

### Speaker

Victor Vakhtel (Voronezh State University)

### Description

During the radiometry of emission fluxes by recording the sequence of counts $\textit{K}({\Delta}{t})$ in time intervals ${\Delta}{t}$ the procedure of forming the sequence of random vectors $(n_{0}{...}n_{i}{...}n_{l})_j$ is performed, where $n_{i}$ $(k_{i}=i)$ is a random number of equal values of $k_{i}$ in one random sample of the size $n=n_{0}+{...}n_{i}+{...}n_{l}$. With a small sample size $n\leq{10}$, a large number of $M>10^{5}$ and the number of different types of $j$ vectors $Q>10^{4}$ statistical analysis of their frequency characteristics is a difficult problem. A particular implementation of type $j$ of the combination of values $n_{i}$ occurs in a vector with a random frequency $M_{j}$, the binomial estimation of which is $MP_{j}$, where $P_{j}$ is a polynomial probability of the vector appearance. To each type of vector $j$, the discrete functionality $ID(-)_{j}=(a_{0}n_{0}+{...}+a_{l}n_{l})$ corresponds unambiguously, where $(a_{0},...,a_{l})$ is a specified non-random vector $1\leq{a_{0}}\leq{...}\leq{a_{l}}$ with integer components $a_{i}$.

Multimodal empirical distributions $M_{j}(ID_{j})$ depending on the values of $a_{j}$ make it possible to unite homogeneous vectors of the corresponding types into peaks without complicated testing of hypotheses about the type of distribution in small samples.

### Primary authors

Alexander Babenko (Voronezh State University) Nikolay Bliznyakov (Voronezh State University) Vladimir Rabotkin (Voronezh State University) Victor Vakhtel (Voronezh State University)

### Presentation materials

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