Abstract
LET U(G|F) denote the utility of the assertion that the distribution of a random vector x is G when it is really F. Although the utility must depend on the context it is interesting to consider what form the functional U might take if it is some form of generalized expectation of v(x,y), defined as the utility of asserting that the value of the random vector is y when it is really x. We assume that v(x,y)≤v(x,x). Natural axioms are (i) if a constant is added to v then the same constant is added to U; (ii) additivity for mutually irrelevant vectors (iii) invariance under non-singular transformations of x: U(G|F) is unchanged if a non-singular transformation x = ψ(x′), y = ψ(y′) is made, subject to the obvious desideratum that the transformed form of v is v(ψ(x′), ψ(y′)).
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References
Good, I. J., J. Roy. Statist. Soc., B, 22, 79 (1960).
Kerridge, D. F., J. Roy. Statist. Soc., B, 23, 184 (1961).
Wald, A., Statistical Decision Functions (Wiley, New York, 1950).
Jaynes, E. T., Phys. Rev., 106, 620 (1957).
Jeffreys, H., Proc. Roy. Soc., A, 186, 453 (1946).
Perks, W., J. Inst. Actuar., 73, 285 (1947).
Good, I. J., in Multivariate Analysis, II (edit. by Krishnaiah, P. R.) (Academic Press, New York, in the press).
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GOOD, I. Utility of a Distribution. Nature 219, 1392 (1968). https://doi.org/10.1038/2191392a0
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DOI: https://doi.org/10.1038/2191392a0
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