Bounds for the generalized Marcum Q-function

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this paper we consider the generalized Marcum Q-function of order ν > 0 real, defined byQν(a,b)=1/aν-1∫b∞tνe-t 2+a2/2Iν-1(at)dt,where a > 0, b ≥ 0 and Iν stands for the modified Bessel function of the first kind. Our aim is to extend some results on the (first order) Marcum Q-function to the generalized Marcum Q-function in order to deduce some new lower and upper bounds. Moreover, we show that the proposed bounds are very tight for the generalized Marcum Q-function of integer order, and we deduce some new inequalities for the more general case of real order. The chief tools in our proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind, which are based on a criterion for the monotonicity of the quotient of two Maclaurin series.

Original languageEnglish
Pages (from-to)2238-2250
Number of pages13
JournalApplied Mathematics and Computation
Volume217
Issue number5
DOIs
Publication statusPublished - Nov 1 2010

    Fingerprint

Keywords

  • Bounds
  • Complementary error function
  • Generalized Marcum Q-function
  • Incomplete gamma function
  • Modified Bessel functions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this