On evaluation of confidence intervals for parameters of log-likelihood and χ2 minimization fits

In this paper, we give equations for statistical fluctuations of fit parameters as functions of statistical fluctuations of the number of events in individual channels of fitted histogram. We use these equations to reconstruct the probability density function (PDF) for the fit parameters and, hence, evaluate the respective confidence intervals if necessary. We also consider a possibility of using the Taylor expansion coefficients of log-likelihood and χ2 as functions of fit parameters in vicinity of their minima for the PDF reconstruction as well.