Compute an interval probability under a bounded uniform model

Define the task

Specify the support endpoints and their units before describing a continuous uniform distribution. The model assigns equal density across a finite interval, so equal-length subintervals within the support have equal probability. Choosing endpoints from the observed sample extremes is a separate estimation decision with consequences for uncertainty.

Carry out the check

Intersect the event interval with the support. Divide the length of this overlap by the total support width. An event wholly outside the support has zero probability. An interval covering the entire support has probability one. Individual endpoints have probability zero in a continuous model, although rounding recorded values can create observed ties at the endpoints.

Worked hypothetical example

For a hypothetical start time uniformly distributed from 2 to 8 minutes, a window from 5 to 10 overlaps the support for three minutes. Its probability is 3/6 or 0.5. A window from 8 to 10 overlaps only at a single endpoint and has probability zero. Check the actual scheduling mechanism before using uniformity to predict arrival or delay patterns.

Method checked 11 November 2026 against R documentation: The Uniform Distribution.

Open the uniform interval overlap probability.