  IceCube is a cubic-kilometer Cherenkov telescope operating at the South Pole.
The main goal of IceCube is the detection of astrophysical neutrinos and the
identification of their sources. High-energy muon neutrinos are observed via
the secondary muons produced in charge current interactions with nuclei in the
ice. Currently, the best performing muon track directional reconstruction is
based on a maximum likelihood method using the arrival time distribution of
Cherenkov photons registered by the experiment's photomultipliers. A known
systematic shortcoming of the prevailing method is to assume a continuous
energy loss along the muon track. However at energies $>1$ TeV the light yield
from muons is dominated by stochastic showers. This paper discusses a
generalized ansatz where the expected arrival time distribution is parametrized
by a stochastic muon energy loss pattern. This more realistic parametrization
of the loss profile leads to an improvement of the muon angular resolution of
up to $20\%$ for through-going tracks and up to a factor 2 for starting tracks
over existing algorithms. Additionally, the procedure to estimate the
directional reconstruction uncertainty has been improved to be more robust
against numerical errors.
