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We present a comparison between Monte Carlo simulations and a semi-analyticalapproach that reproduces the theoretical probability distribution functions ofthe solar neutrino fluxes, stemming from the $pp$, $pep$, $hep$,$^7\mathrm{Be}$, $^8\mathrm{B}$, $^{13}\mathrm{N}$, $^{15}\mathrm{O}$, and$^{17}\mathrm{F}$ source reactions. We obtain good agreement between the twoapproaches. Thus, the semi-analytical method yields confidence intervals thatclosely match those found, based on Monte Carlo simulations, and points towardsthe same general symmetries of the investigated probability distributionfunctions. Furthermore, the negligible computational cost of this method is aclear advantage over Monte Carlo simulations, making it trivial to take newobservational constraints on the input parameters into account.

A Semi-Analytical Computation of the Theoretical Uncertainties of the Solar Neutrino Flux