Random Truncation and Neutrinos

Abstract

We study in this article the energies of neutrinos observed in the Irvine-Michigan-Brookhaven detector near Fairport, Ohio. The chance of observing a neutrino with a given amount of energy is a function of the sensitivity or trigger efficiency of the detector. Because some of the neutrinos were undetected, the distribution of the observed data is randomly truncated. We consider maximum likelihood estimation of the parameters for the randomly truncated normal distribution (as well as a normal model for power transformations). To obtain confidence regions for the parameters, both asymptotic-normal-theory and approximate-likelihood-based confidence regions are constructed. Monte Carlo investigations are used to study the properties of maximum likelihood estimators for randomly truncated normal distributions. The simulation study shows that confidence regions based on the asymptotic normal theory perform very poorly. whereas the approximate-likelihood-based regions provide coverages closer to the nominal level.

KEY WORDS:

• Biased sampling
• EM algorithm
• Maximum likelihood estimation
• Weighted distributions