Choosing a probability distribution

A duration that is fixed by design or set somewhere else.

You know a hard minimum and maximum but have no reason to favour values inside them.

Positive memoryless waits with many short observations and occasional long ones.

Measurements cluster symmetrically around a mean and large deviations are uncommon.

Positive durations formed by several multiplicative effects, producing a right tail.

You can estimate a minimum, most-likely value, and maximum but have little raw data.

Positive right-skewed durations made from accumulated waiting or work stages.

Positive durations where completion or failure likelihood changes with elapsed time.

Heavy-tailed processes where rare extreme durations are part of system risk.

You have observed durations and want to preserve their measured shape.

Only a finite set of durations can occur and each has an observed or chosen weight.

A finite evenly spaced set of values is possible and each should be equally likely.

There are exactly two possible durations tied to a binary outcome.