This paper provides a detailed empirical investigation of the distribution of travel times on an urban road for valuation of travel time variability. Our investigation is premised on the use of a theoretical model with a number of desirable properties. The definition of the value of travel time variability depends on certain properties of the distribution of random travel times that require empirical verification. Applying a range of nonparametric statistical techniques to data giving minute-by-minute travel times for a congested urban road over a period of five months, we show that the standardized travel time is roughly independent of the time of day as required by the theory. Except for the extreme right tail, a stable distribution seems to fit the data well. The travel time distributions on consecutive links seem to share a common stability parameter such that the travel time distribution for a sequence of links is also a stable distribution. The parameters of the travel time distribution for a sequence of links can then be derived analytically from the link level distributions.