Monotonicity properties and bounds for the chi-square and gamma distributions

作者：

Highlights：

• A sharp analysis of the convexity properties of Marcum functions is performed.

• Monotonicity properties for ratios of consecutive Marcum functions are obtained.

• The new bounds for Marcum functions improve previous bounds in large regions.

• New and improved monotonicity properties are obtained in the central case.

• The combined bounds obtained for the central case are superior to previous bounds.

摘要

•A sharp analysis of the convexity properties of Marcum functions is performed.•Monotonicity properties for ratios of consecutive Marcum functions are obtained.•The new bounds for Marcum functions improve previous bounds in large regions.•New and improved monotonicity properties are obtained in the central case.•The combined bounds obtained for the central case are superior to previous bounds.

论文关键词：Generalized Marcum function,Cumulative chi-square and gamma distributions,Bounds,Monotonicity,Convexity

论文评审过程：Available online 6 September 2014.

论文官网地址：https://doi.org/10.1016/j.amc.2014.08.034