  Event-by-event fluctuations in the elliptic-flow coefficient $v_2$ are
studied in PbPb collisions at $\sqrt{s_{_\text{NN}}} =$ 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 $< p_\mathrm{T} <$ 3.0 GeV
and pseudorapidity $| \eta | <$ 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 fluctuation behavior. Bessel-Gaussian and elliptic power fits to
the flow distributions are studied to characterize the initial-state spatial
anisotropy.
