Statistically Dual Distributions and Estimation

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.

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