Fiducial inference: Difference between revisions

Clarified that ω is not regarded as a random variable and its fiducial intervals represent degrees of belief.
(Change "Fisher says" to "Fisher might say")
(Clarified that ω is not regarded as a random variable and its fiducial intervals represent degrees of belief.)
Then Fisher might say that this statement may be inverted into the form
:<math>P\left(\omega < \frac{X}{a}\right) = \alpha .</math>
In this latter statement, ω is now regarded as a [[random variable]] and ''X'' is fixed, whereas previously it was the other way round. This distribution of ω is the ''fiducial distribution'' which may be used to form fiducial intervals that represent degrees of belief.
 
The calculation is identical to the [[pivotal quantity|pivotal method]] for finding a confidence interval, but the interpretation is different. In fact older books use the terms ''confidence interval'' and ''fiducial interval'' interchangeably.{{Citation needed|date=October 2010}} Notice that the fiducial distribution is uniquely defined when a single sufficient statistic exists.
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