This paper deals with statistical modelling of critical clearances which are the main subject of the Gap Acceptance theory. The full report is available here: Full report.
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First, we used appropriate terminology to define a mathematical model of an unsignalized T intersection. Using this model we presented the problem of the partial distribution of clearances of order
$k \in \mathbb{N}_0$ . -
Assuming gamma distribution of clearances and critical clearances we derived a solution to this problem. We later validated this solution by using numerical computations. Further, with the premise of gamma distributed critical clearances, we analytically derived the Siegloch function.
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At last, we verified that the empirical partial distribution of clearances of order
$k \in {0, 1, 2, 3}$ (recorded at three German T intersections) belongs to the family of previously derived partial distribution of clearances. This hypothesis was evaluated by using Pearson’s$\chi$ -squared goodness of fit test.
