A supplement to the Davis–Gut law

Abstract: Let be a sequence of i.i.d. real-valued random variables and set , . Let be a positive nondecreasing function such that . Define for . In this note we prove that if and only if and , where , . When , this result yields what is called the Davis–Gut law. Specializing our result to , , we obtain an analog of the Davis–Gut law. [Copyright &y& Elsevier]