An inequality for characteristic functions

C.R. Heathcote, J.W. Pitman
1972 Bulletin of the Australian Mathematical Society  
The paper is concerned with an extension of the inequality 1 -u{2 n t) < k n [l-u(t)] for u(t) the real part of a characteristic function. The main result is that the inequality in fact holds for all positive integer n and not only powers of 2 . Certain consequences are deduced and a brief discussion is given of the circumstances under which equality holds. Suppose the random variable X has characteristic function Ee = ty(t) with real and imaginary parts respectively u{t) = EcoatX , v(t) = EsintX .
more » ... coatX , v(t) = EsintX .
doi:10.1017/s0004972700044191 fatcat:nr6pup4cbnbrrd23fdhmqynkau