Greenwood (1946), using an L2 distance, and others have addressed the question of detecting a too-linear fit of the occurrence times T0 < T1 < · · · < Tn of a sequence of random events. Two convenient distances are introduced here, then applied to the more challenging problem of detecting too-linear subsequences, where the multiple subsequence effect must be taken into account. Two interpretations of “linear subsequence” are considered.

Key Words: Poisson process, exponential distribution, arrival times, linear sequence, linear subsequence, gap-linear, Dirichlet distribution, product of beta random variables.