I am fitting a distribution with two components, sig and bkg. I have to calculate the ratio of the yield of the two components in a sub-range of the full fitting range. How can I evaluate the uncertainty on that value?

What I am doing is:

bkg_fraction = bkg_pdf.createIntegral(x,x,RangeName='mySubRange')
sig_fraction = sig_pdf.createIntegral(x,x,RangeName='mySubRange')
ratio = yield_bkg.GetVal()*bkg_fraction/(yield_sig.GetVal()*sig_fraction)

Where yield_bkg and yield_bkg are yield parameters of the pdf bkg_pdf and sig_pdf, respectively.

I can evaluate the uncertainty on bkg_fraction with bkg_fraction.getPropagatedError(fit_result,x). But how can I propagate properly to the ratio? I can do analytically, but I don’t know how to access to the the correlation with and between the _fractions.