On Normalization Functions and φ-Families of Probability Distributions

摘要: -families of probability distributions are a general representation to deformed exponential models which brings interesting insight on the geometrical aspects of the distribution family. In the -family, the analogue of the cumulant-generating function is a normalizing function. This function plays an important role in the statistical model and we investigate the behaviour of the function near the boundary of the domain of the parametrization in order to provide the precise conditions of validity of the - family model. We discuss the conditions for existence of the statistical model when considering -functions and the required conditions for the normalization function so we can provide a complete understanding about the investigated family of probability distribution.