

















A noncentral chi-square density is log-concave if the degree of freedom is nu>=2. We complement this known result by showing that, for each 0<nu<2, there exists lambda_nu>0 such that the chi-square with nu degrees of freedom and noncentrality parameter lambda has a decreasing density if lambda <= lambda_nu, and is bi-modal otherwise. The critical lambda_nu is characterized by an equation involving a ratio of modified Bessel functions. When an interior mode exists we derive precise bounds on its location.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。