Estimating minimum gap acceptances for merging motorists

Assume that motorists arrive at a stop sign and wish to merge into traffic on the main road, using the following criterion for making decisions: For each motorist there is a number, X, which is the smallest headway which the motorist will accept before merging into it. For each of these gaps presented to a particular motorist, X is the same, but X varies from motorist to motorist, and has the distribution function FX(x). Assuming the gaps are independent and identically distributed variates, and the merging motorists arrive at times independent of the traffic on the main road, consistent estimates of the moments of X are obtained, using sample values of the accepted and rejected gaps. An estimator of FX(x) is also obtained, without these assumptions. The paper concludes with a numerical analysis using data obtained from an intersection in Sydney.