منابع مشابه
New bounds for the Marcum Q-function
New bounds are proposed for the Marcum -function, which is defined by an integral expression where the 0th-order modified Bessel function appears. The proposed bounds are derived by suitable approximations of the 0th-order modified Bessel function in the integration region of the Marcum -function. They prove to be very tight and outperform bounds previously proposed in the literature. In partic...
متن کاملComputation of the Marcum Q-function
Methods and an algorithm for computing the generalized Marcum Q−function (Qµ(x, y)) and the complementary function (Pµ(x, y)) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics and probability theory , where they are called the non-central chi-square or the non central gamma cumulativ...
متن کاملInequalities for the generalized Marcum Q-function
Keywords: Generalized Marcum Q-function Non-central chi and chi-squared distribution Modified Bessel functions Log-concavity NBU property a b s t r a c t In this paper, we consider the generalized Marcum Q-function of order m > 0 real, defined by Q m ða; bÞ ¼ 1 a mÀ1 Z 1 b t m e À t 2 þa 2 2 I mÀ1 ðatÞdt; where a; b P 0, I m stands for the modified Bessel function of the first kind and the righ...
متن کاملOn Log-concavity of the Generalized Marcum Q Function
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.
متن کاملSolutions to Integrals Involving the Marcum Q-Function and Applications
Novel analytic solutions are derived for integrals that involve the generalized Marcum Q−function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for specific cases of the generic integrals. The offered expressions are both convenient and versatile, which is particularly useful in applications relating to natural sciences and engineering, including w...
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ژورنال
عنوان ژورنال: The Classical Review
سال: 1905
ISSN: 0009-840X,1464-3561
DOI: 10.1017/s0009840x0099187x