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One of the difficulties in calculating the capacity of certain Poisson channels is that <i>H</i>(¿), the entropy of the Poisson distribution with mean <i>¿</i>, is not available in a simple form. In this paper, we derive upper and lower bounds for <i>H</i>(¿) that are asymptotically tight and easy to compute. The derivation of such bounds involves only(More)
Estimates of the closeness between probability distributions measured in terms of certain distances, particularly, the Kolmogorov and the total variation distances are very common in theoretical and applied probability. Usually, the results refer to upper estimates of those distances, even sharp upper bounds in some sense. As far as we know, only a few(More)
1. INTRODUCTION. In his 1974 book entitled " The Life and Times of the Central Limit Theorem, " Adams [1] describes this theorem as " one of the most remarkable results in all of mathematics " and " a dominating personality in the world of probability and statistics. " More than three decades later, his description is not only still pertinent but has also(More)
We give efficient algorithms, as well as sharp estimates, to compute the Kolmogorov distance between the binomial and Poisson laws with the same mean λ. Such a distance is eventually attained at the integer part of λ 1/2 − √ λ 1/4. The exact Kolmogorov distance for λ ≤ 2 − √2 is also provided. The preceding results are obtained as a concrete application of(More)
We obtain explicit upper estimates in direct inequalities with respect to the usual sup-norm distance for Bernstein-type operators. Our approach combines analytical and probabilistic techniques based on representations of the operators in terms of stochastic processes. We illustrate our results by considering some classical families of operators, such as(More)