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. 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)

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