Event-by-event fluctuations in the elliptic-flow coefficient v(2) are studied in PbPb collisions at root S-NN = 5.02 TeV using the CMS detector at the CERN LHC. Elliptic-flow probability distributions p(v(2)) for charged particles with transverse momentum 0.3 < p(T) < 3.0 GeV/c and pseudorapidity vertical bar eta vertical bar < 1.0 are determined for different collision centrality classes. The moments of the p(v(2)) distributions are used to calculate the v(2) coefficients based on cumulant orders 2, 4, 6, and 8. A rank ordering of the higher-order cumulant results and nonzero standardized skewness values obtained for the p(v(2)) distributions indicate non-Gaussian initial-state fluctuations. Bessel-Gaussian and elliptic power fits to the flow distributions are studied to characterize the initial-state spatial anisotropy. (C) 2018 The Author(s). Published by Elsevier B.V.