Comparison of Probability Distributions

摘要: OFTEN, more than one probability distribution is theoretically feasible when considering statistical models for an experiment. The problem of determination the plausible using likelihood procedures (see, example, Sprott and Kalbfleisch, 1969) will be discussed simple case where all observations are made under same response conditions. (Lindsey, 1974, consider this independent variables present.) To do inference, a base model must introduced with which other distributions consideration may compared. derivation follows yields multinomial as model. Several approaches have been suggested in literature to determining number possible best describes set data. Cox (1961, 1962) develops asymptotic Neyman-Pearson ratio tests suggests alternative approach involving combination, either additive or multiplicative, density functions, estimation additional parameters. This further developed by Atkinson (1970). When prior probabilities, both each parameters within models, available, Lindley p. 456) gives posterior odds two Bayes's theorem. applicable (i.e. probabilities available), used methods below.