  In the PHFB model, uncertainties in the nuclear transition matrix elements
for the neutrinoless double-$\beta $ decay of $\ ^{94,96}$Zr, $^{98,100}$Mo,
$^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes within
mechanisms involving light Majorana neutrinos, classical Majorons and sterile
neutrinos are statistically estimated by considering sets of sixteen
(twenty-four) matrix elements calculated with four different parametrization of
the pairing plus multipolar type of effective two-body interaction, two sets of
form factors and two (three) different parameterizations of Jastrow type of
short range correlations. In the mechanisms involving the light Majorana
neutrinos and classical Majorons, the maximum uncertainty is about 15% and in
the scenario of sterile neutrinos, it varies in between approximately 4
(9)%--20 (36)% without(with) Jastrow short range correlations with
Miller-Spencer parametrization, depending on the considered mass of the sterile
neutrinos.

Nuclear Theory