Analysis of experimental statistics of intervals. 1. Equivalence of intervals statistics and of count statistics

The results of experimental checking of equivalence for long sets of intervals statistics between moments of neutrons registration, and statistics of received from them count rates from a detecting block are given. A numerical evaluation of such equivalence is given. Calculated values for experimental data were compared with the corresponding ones, which were received from the model data. As a model data, the sample of numbers which are distributed according to an exponential law, have been used. The volume and mean value of the model data were the same as in experimental ones. The statistical parameters studied were the ratio of the mean square deviation to the mean for the intervals, and the ratio of the variance to the mean for the count rate, that is, respectively for the exponential and Poisson distributions. The theoretical values of these ratios are known and equal to unity. It is shown that when calculating the number of samples from the experimentally measured sample of time intervals in order to obtain a satisfactory uncertainty of the statistical parameters, the exposure time Δ, for which the number of counts is counted, must be in a certain range from Δ_min to Δ_max, which depend on the mean interval value.