UDC:

УДК 53.088, 519.23

Abstract:

We propose a method for statistical comparison of two data sets. The method is

based on the method of statistical comparison of histograms. Usually a one

dimensional test statistic is used as a measure of distinction of data sets. This test

statistic depends on the shape of distributions in data sets. Using the two

dimensional test statistics which is determined via the statistical moments of

distribution produced by the calculation of “the significance of deviations” for the

corresponding points with observed values is proposed in the paper as a distinction

measure between data sets. The significance of deviation in the corresponding

points can be considered as a realization of the random variable which is close to

a standard normal random variable if we observe the same random value in both

data sets. It helps to avoid the dependence of the result on the shape of

distributions. The accuracy of the estimator for the measure of distinction is

determined by the MonteCarlo experiment which, by analogy with the construction

of repeated samples (resampling) in the bootstrap method, it is possible to call

construction of repeated data set (redatasetting). As an estimator of quality of the

decision made, it is proposed to use the value which it is possible to call the

probability that the decision ‘’data sets are various’’ is correct.

References:

1. EXFOR Library. Available at: http://wwwnds.iaea.org/exfor/exfor.htm

2. Barashenkov V.S., Konobeev A.Yu., Korovin Yu.A., Sosnin V.N. Atomnaya Energiya. 1999, no. 87, p. 283.

3. Anrianov A.A., Konobeev A.Yu., Korovin Yu.A., Kuptsov I.S., Stankovskij A.Yu. Izvestiya vuzov. Yadernaya energetika. 2011, no. 2, p. 5.

4. Korovin Yu.A., Maksimushkina A.V. Yadernaya Fizika i Ingeniring. 2014, no. 5, p. 237.

5. Bityukov S.I., Krasnikov N.V., Nikitenko A.N., Smirnova V.V. A method for statistical comparison of histograms. arXiv:1302.2651 2013.

6. Bityukov S.I., Krasnikov N.V., Nikitenko A.N., Smirnova V.V. Vestnik RUDN. Seriya: matematika, informatika, fisika. 2014, no.2, p. 324.

7. Bityukov S., Krasnikov N., Nikitenko A., Smirnova V. Eur.Phys.J.Plus. 2013, no.128:143.

8. Porter F. Testing consistency of two histograms. arXiv:0804.0380 2008.

9. Efron B. Bootstrap methods: another look at the jackknife. Annals of Statistics. 1979, no. 7, p. 1.

10. Bityukov S.I., Krasnikov N.V. Distinguishability of Hypotheses. Nucl.Inst.&Meth. 2004 A534, p. 152.

11. Korovin Yu.A., Maksimushkina A.V. Izvestiya vuzov. Yadernaya energetika. 2014, no. 2, p. 51.