Sufficient Statistics and Orthogonal Parameters

Let be, for a set of n real continuous parameters the probability density function of a random variable x with respect to a σ-finite measure μ on a σ-algebra of subsets of the sample space . If x ; is a continuous random variable, μ will be Lebesgue measure on the Borel sets of a Euclidean sample space and, if x is discrete, μ will be counting measure on the class of all sets of a countable sample space. The parameters α i are said to be orthogonal (Jeffreys (3), pp. 158,184) if .