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- W1552341214 abstract "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." @default.
- W1552341214 created "2016-06-24" @default.
- W1552341214 creator A5075536049 @default.
- W1552341214 date "2011-06-26" @default.
- W1552341214 modified "2023-09-23" @default.
- W1552341214 title "The Shape of the Noncentral Chi-square Density" @default.
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- W1552341214 doi "https://doi.org/10.48550/arxiv.1106.5241" @default.
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