Out-of-home activities are engaged within time – space prisms, but the prisms themselves are unobservable. In this paper, stochastic frontier models with observed departure and arrival times as dependent variables are formulated to locate time – space prism vertices. Two possible distributions often used in frontier models for one-sided disturbance terms, the half-normal distribution and exponential distribution, are examined better to represent observed behavior. The locations of morning prism origin vertices and evening prism terminal vertices on working days and nonworking days are estimated with an empirical dataset obtained in southeast Florida. The results suggest that the exponential distribution has a better goodness of fit, but the coefficient estimates of explanatory variables are similar between models with the two distributions, suggesting that the model parameter estimates are robust regardless of the assumptions regarding the distribution of the one-sided random disturbance. It is found that the average heights of the morning prism before work and the evening prism after work on working days are estimated at about 2.5 hours and about 3 hours, respectively. It is also found that part-time workers have prism heights that are on average larger by half an hour than those of full-time workers on working days, and smaller by 1.5 hours on nonworking days.
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