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.