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In statistical inference, the concept of a confidence distribution (CD) has often been loosely referred to as a distribution function on the parameter space that can represent confidence intervals of all levels for a parameter of interest. Historically, it has typically been constructed by inverting the upper limits of lower sided confidence intervals of all levels, and it was also commonly associated with a fiducial interpretation (fiducial distribution), although it is a purely frequentist concept. A confidence distribution is NOT a probability distribution function of the parameter of interest, but may still be a function useful for making inferences.

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rdfs:label	Confidence distribution (en)
rdfs:comment	In statistical inference, the concept of a confidence distribution (CD) has often been loosely referred to as a distribution function on the parameter space that can represent confidence intervals of all levels for a parameter of interest. Historically, it has typically been constructed by inverting the upper limits of lower sided confidence intervals of all levels, and it was also commonly associated with a fiducial interpretation (fiducial distribution), although it is a purely frequentist concept. A confidence distribution is NOT a probability distribution function of the parameter of interest, but may still be a function useful for making inferences. (en)
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Link from a Wikipage to another Wikipage	Bayesian inference Ronald Fisher Random measure Confidence interval Parametric statistics Estimator Ellipse Multivariate normal distribution Confidence region Statistical inference Likelihood function Stata P-value Plane (geometry) Statistical parameter Measurable space Estimation theory C. R. Rao Normal distribution Journal of the Royal Statistical Society Pearson product-moment correlation coefficient Statistical power Hilbert space Asymptotic distribution Covariance matrix Coverage probability Jerzy Neyman Bootstrapping (statistics) Frequentist inference Microsoft Excel R (programming language) Fisher transformation Random compact set Fiducial distribution Point estimate Point estimator Prior distribution Posterior distribution
Link from a Wikipage to an external page	http://djafari.free.fr/MaxEnt2010/slide/011.pdf https://academic.oup.com/biomet/article-abstract/92/3/529/218911 https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.12000 https://doi.org/10.1017/CBO9781139046671 https://link.springer.com/content/pdf/10.1007/978-1-4614-1412-4_19.pdf https://www.researchgate.net/profile/Jan_Hannig/publication/228369297_On_Generalized_Fiducial_Inference/links/00b4951cad797c1ccd000000.pdf http://projecteuclid.org/DPubS%3Fservice=UI&version=1.0&verb=Display&handle=euclid.imsc/1331731621 https://pubag.nal.usda.gov/%3Fpage=17938&per_page=100&search_field=all_fields
sameAs	Confidence distribution Confidence distribution Confidence distribution
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has abstract	In statistical inference, the concept of a confidence distribution (CD) has often been loosely referred to as a distribution function on the parameter space that can represent confidence intervals of all levels for a parameter of interest. Historically, it has typically been constructed by inverting the upper limits of lower sided confidence intervals of all levels, and it was also commonly associated with a fiducial interpretation (fiducial distribution), although it is a purely frequentist concept. A confidence distribution is NOT a probability distribution function of the parameter of interest, but may still be a function useful for making inferences. In recent years, there has been a surge of renewed interest in confidence distributions. In the more recent developments, the concept of confidence distribution has emerged as a purely frequentist concept, without any fiducial interpretation or reasoning. Conceptually, a confidence distribution is no different from a point estimator or an interval estimator (confidence interval), but it uses a sample-dependent distribution function on the parameter space (instead of a point or an interval) to estimate the parameter of interest. A simple example of a confidence distribution, that has been broadly used in statistical practice, is a bootstrap distribution. The development and interpretation of a bootstrap distribution does not involve any fiducial reasoning; the same is true for the concept of a confidence distribution. But the notion of confidence distribution is much broader than that of a bootstrap distribution. In particular, recent research suggests that it encompasses and unifies a wide range of examples, from regular parametric cases (including most examples of the classical development of Fisher's fiducial distribution) to bootstrap distributions, p-value functions, normalized likelihood functions and, in some cases, Bayesian priors and Bayesian posteriors. Just as a Bayesian posterior distribution contains a wealth of information for any type of Bayesian inference, a confidence distribution contains a wealth of information for constructing almost all types of frequentist inferences, including point estimates, confidence intervals, critical values, statistical power and p-values, among others. Some recent developments have highlighted the promising potentials of the CD concept, as an effective inferential tool. (en)
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is Link from a Wikipage to another Wikipage of	Probability box Pearson correlation coefficient Point estimation Correlation Glossary of engineering: M–Z Statistical inference Nils Lid Hjort Exponential distribution Coverage probability Fiducial inference Tore Schweder Confidence Distribution List of statistics articles Fisher transformation
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