Talk:Prediction interval

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I'm not sure about the line "where Ta is the 100(1 − (p/2))th percentile of Student's t-distribution..." for a 100p% prediction interval. For example, for a 90% prediction interval that would be the 55th percentile, which doesn't sound right - or am I missing something?

Perhaps it should instead read "where Ta is the 100(1 − (α/2))th percentile of Student's t-distribution..." for a 100(1-α)% interval, also replacing p by 1-α in the line above (i.e. α is the error rate in the prediction, whereas p was the success rate). For a 90% prediction interval (α=0.1) that would mean using the 95th percentile, which sounds more reasonable.

For possible support for this formulation see http://www.amstat.org/publications/jse/secure/v8n3/preston.cfm which defines α in the same way and uses the 100(α/2)th and 100(1-(α/2))th percentiles of a general distribution. Also http://www.math.umd.edu/~jjm/tpredictionintervals.pdf, which uses the 100(α/2)th percentile of the t-distribution - I assume that the choice of 100(α/2)th or 100(1-(α/2))th percentile depends on how your t-distribution tables are written.

Alternatively, the definition of p as a success rate in the article could be retained by referring to the 100((1+p)/2)th percentile of the t-distribution, in which case the error rate α would not need to be introduced.

Richard J Price 10:54, 22 March 2007 (UTC)