Large deviations of probability rank
Proceedings of the International Symposium on Information Theory, IEEE 2000
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Consider a pair of random variables (X,Y) with distribution P. The probability rank function is defined so that G(x|y) = 1 for the most probable outcome x conditional on Y = y, G(x|y) = 2 for the second most probable outcome, and so on, resolving ties between elements with equal probabilities arbitrarily. The function G was considered in  in the context of finding the unknown outcome of a random experience by asking question of the form 'Is the outcome equal to x?' sequentially until the actual outcome is determined. The primary focus in , and the subsequent works , , was to find tight bounds on the moments E[G(X|Y)θ]. The present work is closely related to these works but focuses more directly on the large deviations properties of the probability rank function.
Probability rank function
Convergence of numerical methods
Probability density function
Communication channels (information theory)