Statistical analysis for the neutrinoless double- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> -decay matrix element of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Ca</mml:mi><mml:mprescripts /><mml:none /><mml:mn>48</mml:mn></mml:mmultiscripts></mml:math>

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