Editing Prediction interval (section)

=== Conformal Prediction ===
{{Main article|conformal prediction}}
In general the conformal prediction method is more general.
Let us look at the special case of using the minimum and maximum as boundaries for a prediction interval:
If one has a sample of identical random variables {''X''<sub>1</sub>,&nbsp;...,&nbsp;''X''<sub>''n''</sub>}, then the probability that the next observation ''X''<sub>''n''+1</sub> will be the largest is 1/(''n''&nbsp;+&nbsp;1), since all observations have equal probability of being the maximum. In the same way, the probability that ''X''<sub>''n''+1</sub> will be the smallest is 1/(''n''&nbsp;+&nbsp;1). The other (''n''&nbsp;&minus;&nbsp;1)/(''n''&nbsp;+&nbsp;1) of the time, ''X''<sub>''n''+1</sub> falls between the [[sample maximum]] and [[sample minimum]] of the sample {''X''<sub>1</sub>,&nbsp;...,&nbsp;''X''<sub>''n''</sub>}. Thus, denoting the sample maximum and minimum by ''M'' and ''m,'' this yields an (''n''&nbsp;&minus;&nbsp;1)/(''n''&nbsp;+&nbsp;1) prediction interval of [''m'',&nbsp;''M''].{{citation needed|reason=are we sure it's (n-1)/n+1) and not (n-2)/n+1)|date=January 2025}}

Notice that while this gives the probability that a future observation will fall in a range, it does not give any estimate as to where in a segment it will fall – notably, if it falls outside the range of observed values, it may be far outside the range. See [[extreme value theory]] for further discussion. Formally, this applies not just to sampling from a population, but to any [[exchangeable sequence]] of random variables, not necessarily independent or [[identically distributed]].