Neutrinoless double beta decay (0νββ) nuclear matrix elements (NME) are the object of many theoretical calculation methods, and are very important for analysis and guidance of a large number of experimental efforts. However, there are large discrepancies between the NME values provided by different methods. In this paper we propose a statistical analysis of the 48Ca 0νββ NME using the interacting shell model, emphasizing the range of the NME probable values and its correlations with observables that can be obtained from the existing nuclear data. Based on this statistical analysis with three independent effective Hamiltonians we propose a common probability distribution function for the 0νββ NME, which has a range of (0.45 - 0.95) at 90\% confidence level of, and a mean value of 0.68.

We study two-neutrino (2νββ) and neutrinoless double-beta (0νββ) decays in the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) frameworks. Calculating the decay of several dozens of nuclei ranging from calcium to xenon with the shell model, and of ββ emitters with a wide range of proton-neutron pairing strengths in the pnQRPA, we observe good linear correlations between 2νββ- and 0νββ-decay nuclear matrix elements for both methods. We then combine the correlations with measured 2νββ-decay half-lives to predict 0νββ-decay matrix elements with theoretical uncertainties based on our systematic calculations. Our results include two-body currents and the short-range 0νββ-decay operator.