ISSN:
1420-8903
Keywords:
Primary 39B40
;
Secondary 62CO5
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Using recent results of Járai we show that the measurable solutions of the functional equationf(x 1 y 1,...,x n y n )f((1−x 1)(1−y 1),..., (1−x n )(1−y n ))=f(x 1(1−y 1),...,x n (1 − (y n ))f(y 1(1−x 1),...,y n(1 −x n )), wheref: (0, 1) n → (0, ∞) and 0〈x i ,y i 〈1,i=1,...,n, are of the form $$f(x_1 ,...,x_n ) = c \exp \left( {\sum\limits_{i = 1}^n {a_i (x_1 - x_1^2 ))} \prod\limits_{i = 1}^n {x_i^{b_1 } ,} } \right.$$ wherec〉0,a 1,...,a n andb 1,..., b are arbitrary real constants. This result enables one to characterize certain independence-preserving methods of aggregating probability distributions over four alternatives.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02311296
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