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\title{THE TRANSFORM BETWEEN THE SPACE OF OBSERVED VALUES AND THE SPACE
OF POSSIBLE VALUES OF THE PARAMETER}

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\author{\underline{Sergey I. Bityukov}$^{1}$, Nikolai V. Krasnikov$^{2}$,
Vera V. Smirnova$^{1}$\\
        (1)  Institute for high energy physics, 142281 Protvino, Russia\\
        (2)  Institute for nuclear research RAS, Moscow, Russia\\
        (e-mail: Serguei.Bitioukov@cern.ch, http://home.cern.ch/bityukov)
       }

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\begin{abstract}
\noindent
In ref~[1] the notion of statistically dual distributions is 
introduced. The reconstruction of confidence density~[2] for the
location parameter for several pairs of statistically dual distributions
(Poisson and Gamma, normal and normal, Cauchy and Cauchy, Laplace
and Laplace) in the case of single observation of the random variable is 
an unique. It allows to introduce the Transform between the space of
observed values and the space of possible values of the parameter.
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\medskip\noindent{References: }

[1] S.I. Bityukov et al. e-Print: math.ST/0411462; S.I. Bityukov et al. \\
    Proc. of Conf. PhyStat'05,
http://www.physics.ox.ac.uk/phystat05/proceedings/

[2] S.I. Bityukov et al., AIP Conf.Proc. 803 (2005) 398-402

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\medskip\noindent{Key Words: }
{Uncertainty, Measurement, Estimation}

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