Share This Article:

Statistically Dual Distributions and Estimation

Abstract Full-Text HTML XML Download Download as PDF (Size:348KB) PP. 963-968
DOI: 10.4236/am.2014.56091    3,161 Downloads   4,242 Views   Citations


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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Bityukov, S. , Krasnikov, N. , Nadarajah, S. and Smirnova, V. (2014) Statistically Dual Distributions and Estimation. Applied Mathematics, 5, 963-968. doi: 10.4236/am.2014.56091.


[1] Bityukov, S.I., Krasnikov, N.V., Smirnova, V.V. and Taperechkina, V.A. (2006) Statistically Dual Distributions in Statisticalinference. In: Lyons, L. and Unel, M.K., Eds., Proceedings of Statistical Problems in Particle Physics, Astrophysics and Cosmology, Imperial College Press, Oxford, England, 102.
[2] Bernardo, J.M. and Smith, A.F.M. (1994) Bayesian Theory. John Wiley and Sons, Chichester.
[3] Bityukov, S.I. (2002) On the Signal Significance in the Presence of Systematic and Statistical Uncertainties. Journal of High Energy Physics, 09, 060.
[4] Jaynes, E.T. (1983) Confidenceintervals vs Bayesian Intervals. In: Rosenkrantz, R.D., Ed., E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics, D. Reidel Publishing Company, Dordrecht, 165.
[5] Frodesen, A.G., Skjeggestad, O. and Toft, H. (1979) Probability and Statistics in Particle Physics. Universitetsforlaget, Bergen-Oslo-Tromso, 97.
[6] Cousins, R.D (1995) Why Isn’t Every Physicist a Bayesian American Journal of Physics, 63, 398.
[7] Bityukov, S.I., Krasnikov, N.V. and Taperechkina, V.A. (2000) Confidence Intervals for Poisson Distribution Parameter. Preprint IFVE 2000-61, Protvino.
[8] Casella, G. and Berger, R.L. (2001) Statistical Inference. 2nd Edition, Duxbury Press.
[9] Efron, B. (1998) R. A. Fisher in the 21st Century. Statistical Science, 13, 95.
[10] Xie, M. and Singh, K. (2013) Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review. International Statistical Review, 81, 3-39.
[11] Schweder, T. and Hjort, N.L. (2003) Frequentist Analogies of Priors and Posteriors, Econometrics and the Philosophy of Economics. Princeton University Press, Princeton, 285.
[12] Bityukov, S., Krasnikov, N., Nadarajah, S. and Smirnova, V. (2010) Confidence Distributions in Statistical Inference. AIP Conference Proceedings, 130, 346.
[13] Fisher, R.A. (1930) Inverse Probability. Proceedings of the Cambridge Philosophical Society, 26, 528.
[14] Eadie, W.T., Drijard, D., James, F.E., Roos, M. and Sadoulet, B. (1971) Statistical Methods in Experimental Physics. North Holland, Amsterdam.
[15] Bityukov, S.I., Medvedev, V.A., Smirnova, V.V. and Zernii, Yu.V. (2004) Experimental Test of the Probability Densityfunction of True Value of Poisson Distribution Parameter by Single Observation of Number of Events. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 534, 228-231.
[16] Blackwell, M., Honaker, J. and King, G. (2012) Multiple Overimputation: A Unified Approach to Measurement Error and Missing Data. Political Methodology, Committee on Concepts and Methods, Working Paper Series, Paper 36.
[17] Bityukov, S.I., Krasnikov, N.V., Smirnova, V.V. and Taperechkina, V.A. (2007) The Transform between the Space of Observed Values and the Space of Possible Values of the Parameter. Proceedings of Science, PoS (ACAT) 062.

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.