On the Monotonicity, Log-Concavity, and Tight Bounds of the Generalized Marcum and Nuttall $Q$-Functions
نویسندگان
چکیده
منابع مشابه
On the monotonicity, log-concavity and tight bounds of the generalized Marcum and Nuttall Q-functions
In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q−functions. More precisely, a simple probabilistic method is firstly given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum Q−function and its deformations is established with respect to each of the three parameters. Sinc...
متن کاملOn the Monotonicity, Log-Concavity, and Tight Bounds of the Generalized Marcum and Nuttall -Functions
In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall -functions. More precisely, a simple probabilistic method is first given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum -function and its deformations is established with respect to each of the three parameters. Since th...
متن کاملOn the Monotonicity of the Generalized Marcum and Nuttall Q-Functions
Monotonicity criteria are established for the generalized Marcum Q-function, QM (α, β), the standard Nuttall Qfunction, QM,N (α, β), and the normalized Nuttall Q-function, QM,N (α, β), with respect to their real order indices M,N . Besides, closed-form expressions are derived for the computation of the standard and normalized Nuttall Q-functions for the case when M,N are odd multiples of 0.5 an...
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It is shown that, if ν ≥ 1/2 then the generalized Marcum Q function Qν(a, b) is log-concave in b ∈ [0,∞). This proves a conjecture of Sun, Baricz and Zhou (2010). We also point out relevant results in the statistics literature.
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2010
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2009.2039048