UC Irvine

If f and g are nonvanishing characteristic functions the functional equation g(s)g(t)g(−s − t) = f(as)f(at)f(−as − at) implies g(s) = eibsf(as), i.e., f and g corresponding to probability distributions of the same type. It is shown here that when f and g are allowed to vanish this equation also has solutions in which f and g correspond to distributions of different types. The practical implication is that there are nonequivalent. Thurstone models which cannot be discriminated by any choice experiment with three objects.