Summary
A notion of distribution form with an intuitive interpretation has had a long presence in statistical writings: “the variable has a normal distribution”, “the lifetime is Weibull”. This paper examines this notion of distribution form and presents a formalization of it. For purposes of statistical modelling (Fraser, 1979) the objectivity of the distribution form is of central concem. Three criteria are examined which relate to this objectivity. Each is shown to require the same restriction on the determination of distribution form, namely, that the class of possible response presentations should have closure properties under composition, that is, be group like. This paper examines the foundational support for the use of the transformation model investigated in Brenner and Fraser (1979).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brenner, David and Fraser, D. A. S. (1979): On foundations for conditional probability with statistical models— when is a class of functions a function. Statistische Hefte 20, 148–159.
Fraser, D. A. S. (1976): Probability and Statistics, Theory and Applications, Toronto, University of Toronto Textbook Store.
Fraser, D. A. S. (1979): Inference and Linear Models, New York City, McGraw Hill.
Rights and permissions
About this article
Cite this article
Brenner, D., Fraser, D.A.S. The identification of distribution form. Statistische Hefte 21, 296–304 (1980). https://doi.org/10.1007/BF02932888
Issue Date:
DOI: https://doi.org/10.1007/BF02932888