A Data-Driven Method for Reconstructing a Distribution from a Truncated Sample with an Application to Inferring Car-Sharing Demand

Abstract

This paper proposes a method to recover an unknown probability distribution given a censored or truncated sample from that distribution. The proposed method is a novel and conceptually simple detruncation method based on sampling the observed data according to weights learned by solving a simulation-based optimization problem; this method is especially appropriate in cases where little analytic information is available but the truncation process can be simulated. The proposed method is compared with the ubiquitous maximum likelihood estimation (MLE) method in a variety of synthetic validation experiments, where it is found that the proposed method performs slightly worse than perfectly specified MLE and competitively with slightly misspecified MLE. The practical application of this method is then demonstrated via a pair of case studies in which the proposed detruncation method is used alongside a car-sharing service simulator to estimate demand for round-trip car-sharing services in the Boston and New York metropolitan areas.