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Let say we have a 95% prediction interval, versus 95%/99% tolerance interval, which one is wider?

A. PI always wider than TI
B. TI always wider than PI
C. Depends on sample you get

Thanks!

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I believe the tolerance interval at 50% confidence is equal to the prediction interval, so the tolerance interval will always be larger.

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    $\begingroup$ It would be nice to read the reason for that belief. An attempt at a rigorous explanation might uncover the assumptions you are implicitly making and the conditions under which your conclusion is correct. $\endgroup$ Commented Sep 1, 2016 at 15:49
  • $\begingroup$ Are you saying that this is an incorrect statement? I was reading up on tolerance intervals a few months ago, and swear I read this somewhere. $\endgroup$ Commented Sep 2, 2016 at 2:33
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    $\begingroup$ First, there are many kinds of tolerance intervals and many ways to construct them, so you need to indicate which one you have in mind and for what model. Second, 50% confidence means your interval has a 50% chance of covering a specified proportion of the distribution. If that interval is usually much wider than that proportion, but only rarely narrower, then on the average it can exceed that proportion. This suggests its performance as a prediction interval will not be at the intended level. Therefore a specific, clear analysis connecting TIs to PIs looks needed here. $\endgroup$ Commented Sep 2, 2016 at 13:15

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