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Introduction. The mathematical model that has been found convenient for most statistical problems contains a sample space X of elements x endowed with an appropriate σ-field of sets over which is given a family of probability measures. These measures are indexed by a quantity, θ, called a parameter, belonging to the parameter space ϴ. The values x are referred to variously as the sample, observations or data. Notice that θ is merely an index for the various probabilities and that as a result this model includes nonparametric statistics, the special techniques in that field being necessitated by the complexity of the space ϴ which, for example, may include all distributions on the real line.
D. V. Lindley (Sat,) studied this question.