Bounds for the symmetric difference of generalized Marcum Q-functions

摘要

Recently, an approximation for large values of a and b for the symmetric difference of Marcum Q-functions Q(a, b) was given in [1] in the case of integer order, i.e. when v = n ϵ N. Motivated by this result, in this note we study the symmetric difference of Marcum Q-functions Q(a, b) of real order v ≥ 1 for the parameters a > b > 0. Our aim is to use some of the lower and upper bounds of the Marcum Q-function that appear in the literature to obtain some tight bounds for the symmetric difference. Another approach, presented in this note, is to investigate the difference via closed forms of the Marcum Q-function.