I perform fit of histogram using gauss for signal and RooChebychev as a background. How can I guarantii that such background won’t be negative (in any point)?
That is indeed difficult with Chebychev polynomials.
The latest ROOT version (5.23/04) contains RooFit 2.98 which
has implements Bernstein polynomials in class RooBernstein.
Bernstein polynomials basis functions are all positive definite by
construction, so a Bernstein polynomial can be defined to be positive definite by simply choosing the ranges of the coefficients to be
[0,1] (i.e. non-negative)