We construct a Malmquist productivity index based on stochastic non-parametric envelopment of data (StoNED) method, and we study how the distributional assumptions in the second StoNED stage affect productivity change and its decompositions. Our discussion show that the distributional assumptions do not affect the estimates of overall productivity change and scale efficiency change, but that estimates of efficiency change and technical change are affected. Data on Norwegian electricity distribution companies is used to illustrate our discussion.