For the muon g-2 experiment at BNL a simple procedure was developed for analytical evaluation of statistical errors and correlations of parameters for the fit of time distribution of decay electrons with 5-parameter function n(t)=n(0)*exp(-t/tau)*(1+A*cos(wt+phi)).

 From 5 parameters (n(0),tau,A,w,phi) the frequency of g-2 oscillations w is the most important since w is one of two numbers (along with magnetic field) to be measured precisely (at sub ppm level) in this experiment.  It was shown that parameters w and phi are correlated and knowledge of the phase of g-2 oscillations phi at the moment of injection of the muon beam into storage ring can be used to improve statistical accuracy of frequency w. The proper formula for that case was derived.

 Methods of statistical analysis were used to find shifts of parameters of the 5-parameters function due to presence of small background of arbitrary time dependence. Some systematic errors for the muon g-2 frequency w were estimated.      The procedure, developed for statistical analysis for the muon g-2 experiment, was applied for statistical analysis of Breit-Wigner (nonrelativistic and relativistic) and Gaussian distributions.

 

 A simple method to search for presence of small periodic background with  known period is also presented. This method was developed for monitoring  of the so called AGS flashlets background for the muon g-2 experiment at  BNL and presently is hardly been using. It's based on "folding" of the time distribution of decay positrons into one AGS period of 2.694 usec. For such applications this method supersedes the Furier analysis method.