IEEE Transactions on Information Theory
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Abstract
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.Since the Nuttall Q-function has similar probabilistic interpretations as the generalized Marcum Q-function, we deduce the log-concavity of the Nuttall Q-function.By exploiting the log-concavity of these two functions, we propose new tight lower and upper bounds for the generalized Marcum and Nuttall Q-functions.Our proposed…
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Topics & keywords
Keywords
- Computer science
- Information theory
- Computer security
- Mathematics
- Statistics
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