Statistically dual distributions and conjugate families
Sergei I. Bityukov · AIP conference proceedings · 2005
The notion of statistically dual distributions was recently introduced. The reconstruction of confidence density 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 is the evidence that these distributions belong to conjugate families. Also, in paper the clear frequentist sense of the confidence density is shown.