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Statistically Dual Distributions and Estimation
Institute for High Energy Physics, Protvino, Russia
Institute for Nuclear Research RAS, Moscow, Russia
School of Mathematics, University of Manchester, Manchester, UK
Institute for High Energy Physics, Protvino, Russia
- 1 Institute for High Energy Physics, Protvino, Russia
- 2 Institute for Nuclear Research RAS, Moscow, Russia
- 3 School of Mathematics, University of Manchester, Manchester, UK
- 4 Institute for High Energy Physics, Protvino, Russia
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Abstract
The reconstruction of a parameter by the measurement of a random variable depending on the parameter is one of the main tasks in statistics. In statistical inference, the concept of a confidence distribution and, correspondingly, confidence density 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. In this short note, the notion of statistically dual distributions is discussed. Based on properties of statistically dual distributions, a method for reconstructing the confidence density of a parameter is proposed.
KeywordsDistribution TheoryConfidence DistributionMeasurementError TheoryData Analysis: Algorithms and ImplementationData Management
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