Simple bounds for the generalised Marcum Q-function

摘要

This paper proposes new bounds for the generalised Marcum Q-function Q_v(a,b) that involve the normalised incomplete gamma functions. The bounds are useful for (i) a ≤ a_0, b ∈ [0, ∞) and (ii) b ≤ b_0, a ∈ [0, ∞), where a_0, b_0 approx- 1. Numerical results are presented to illustrate the sharpness of the bounds and provide a comparison with existing bounds in the literature.