### Speaker

### 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.