A statistical analysis of angular distribution of neutrino events observed in Kamiokande II and IMB detectors from supernova SN 1987 A

A detailed statistical analysis of angular distribution of neutrino events observed in Kamiokande II and IMB detectors on UT 07∶35, 2/23'87 is carried out. Distribution functions of the mean scattering angles in the reactions \(\bar \upsilon _e p \to e^ + n\) andve→ve are constructed with account taken of the multiple Coulomb scattering and the experimental angular errors. The Smirnov and Wald-Wolfowitz run tests are used to test the hypothesis that the angular distributions of events from the two detectors agree with each other. We test with the use of the Kolmogorov and Mises statistical criterions the hypothesis that the recorded events all represent \(\bar \upsilon _e p \to e^ + n\) inelastic scatterings. Then the Neyman-Pearson test is applied to each event in testing the hypothesis \(\bar \upsilon _e p \to e^ + n\) against the alternativeve→ve. The hypotheses that the number of elastic events equalss=0, 1, 2, ... against the alternativess≠0, 1, 2, ... are tested on the basis of the generalized likelihood ratio criterion. The confidence intervals for the number of elastic events are also constructed. The current supernova models fail to give a satisfactory account of the angular distribution data.