Prediction Interval

A prediction interval is a statistical interval constructed from observed data to contain a future observation with a specified coverage probability. If denotes the observed sample and a future observation from the assumed model, a two-sided prediction interval satisfies

for every parameter value in its stated range.

A prediction interval accounts for both uncertainty in estimated parameters and the random variation of the future observation. It therefore differs from a confidence interval for a population parameter. It also differs from a tolerance interval, which is designed to contain a specified proportion of the population with a stated confidence level.