On histogram optimization problem for spectral distributions

The paper describes a method of the optimization of the selection of parameters of a histogram(bin) for a very large class of regressions - those of spectral distributions is described. It is shown that for a regression s(x) the minimal statistical errors are given by bins of equal weights; they are such intervals Xk that the integrals of s(x) over them are equal for any pair of indexes (k, j), j ≠ k; whereas the minimal errors of the representation of a function by a histogram are obtained, when the abscissa of any histogram ordinate is assigned to the value, where the function is equal to its integral mean (while using the quadratic metrics) or to the amplitude mean (while using the uniform metrics). In both cases this abscissa may differ from the middle of the bin. The described method of the optimation has been applied to the most frequently used models of spectral functions - exponential, Gaussian and Lorentzian