On confidence limits and statistical convergence of Monte Carlo point-flux estimators with unbounded variance

The problem of analyzing the statistical error of Monte Carlo point-flux estimators with unbounded variance is considered. The results are based on the generalization of the classical limit theorem for summands of identically-distributed random variables on the unbounded-variance case. The Lévy representation of the characteristic functions of stable attracting distributions is implemented. The explicit expression of the stable attracting probability density function for the uncollided point-flux estimates is obtained and the corresponding cumulative probability function is tabulated. It is shown that a 1 x singularity of an unbounded-variance point-flux estimator in the vicinity of the detector point leads to 1 N ^{1 2} convergence to the normal law. The procedure of estimation of confidence limits and statistical accuracy of unbounded-variance point-flux estimators for intermediate sample size is discussed. The results may be utilized for the calculation of statistical error of Monte Carlo calculations of flux at a point.