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In ref [math.ST/0411462] the notion of statistically dual distributions isintroduced. The reconstruction of confidence density [AIP ConferenceProceedings 803 (2005) 398] for the location parameter for several pairs ofstatistically dual distributions (Poisson and Gamma, normal and normal, Cauchyand Cauchy, Laplace and Laplace) in the case of single observation of therandom variable is a unique. It allows to introduce the Transform between thespace of observed values and the space of possible values of the parameter.

The Transform between the space of observed values and the space of possible values of the parameter