International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Fiducial Inference

  • Jan Hannig
  • Hari Iyer
  • Thomas C. M. Lee
Reference work entry


The origin of Generalized Fiducial Inference can be traced back to R. A. Fisher (Fisher 1930, 1933, 1935) who introduced the concept of a fiducial distribution for a parameter, and proposed the use of this fiducial distribution, in place of the Bayesian posterior distribution, for interval estimation of this parameter. In the case of a one-parameter family of distributions, Fisher gave the following definition for a fiducial density f( θ | x) of the parameter based on a single observation x for the case where the cdf F( x | θ) is a monotonic decreasing function of θ:
$$f(\theta /x) = -\frac{\partial F(x\vert \theta )} {\partial \theta } .$$
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References and Further Reading

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jan Hannig
    • 1
  • Hari Iyer
    • 2
  • Thomas C. M. Lee
    • 3
  1. 1.The University of North Carolina at Chapel HillChapel HillUSA
  2. 2.Colorado State UniversityFort CollinsUSA
  3. 3.The University of California at DavisDavisUSA