What is a fiducial confidence interval?

A fiducial confidence interval is a confidence interval based on fiducial statistical theory, which considers unknown population parameters to be random variables. Fiducial confidence intervals are primarily used in probit analysis.

For a 100(x)% fiducial confidence interval, the probability that the population parameter falls within the interval is (x).

This interpretation is fundamentally different from that of standard confidence intervals. Standard confidence intervals do not consider population parameters to be random variables, but fixed values, and consider the confidence interval itself to be random, because the interval is derived from a random sample.

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