Non-Parametric Method for Testing the Exponential Small Volume Data for Purity

Abstract

In many innovative physical experiments such (as, e.g., the synthesis of superheavy elements) the statistics of the observed data is often small and there is not enough of the a priori information about the parameters of their distribution function. Here the first important problem is to get sure that the data is “pure”, i.e. the events are produced by one factor and not by several. Although the available methods for the problem solution are numerous, the most popular methods using the regressions or likelihood relations, for the above reason are not expedient for our case. The non-parametrical tests having the reputation of parameter-independent and little-sensitive to the data statistics, seem here to be the most suitable. The paper suggests such a non-parametrical criterion for purity of the exponential event distribution: the ratio of the sample median and the sample mean. Actually the method can be generalized to be used for some other distributions, first of all, the normal one.