  In ref [math.ST/0411462] the notion of statistically dual distributions is
introduced. The reconstruction of confidence density [AIP Conference
Proceedings 803 (2005) 398] 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 a unique. It allows to introduce the Transform between the
space of observed values and the space of possible values of the parameter.
