Analytical depoissonization and its applications
Theoretical Computer Science
Singularity analysis and asymptotics of Bernoulli sums
Theoretical Computer Science
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
On the capacity of the discrete-time poisson channel
IEEE Transactions on Information Theory
Monotonic convergence in an information-theoretic law of small numbers
IEEE Transactions on Information Theory
Entropy computations via analytic depoissonization
IEEE Transactions on Information Theory
Binomial and Poisson distributions as maximum entropy distributions
IEEE Transactions on Information Theory
Maximum entropy versus minimum risk and applications to some classical discrete distributions
IEEE Transactions on Information Theory
Rate of convergence to Poisson law in terms of information divergence
IEEE Transactions on Information Theory
Entropy and the law of small numbers
IEEE Transactions on Information Theory
Mutual Information and Conditional Mean Estimation in Poisson Channels
IEEE Transactions on Information Theory
On the Maximum Entropy Properties of the Binomial Distribution
IEEE Transactions on Information Theory
Thinning, entropy, and the law of thin numbers
IEEE Transactions on Information Theory
Hi-index | 754.92 |
One of the difficulties in calculating the capacity of certain Poisson channels is that H(λ), the entropy of the Poisson distribution with mean λ, is not available in a simple form. In this paper, we derive upper and lower bounds for H(λ) that are asymptotically tight and easy to compute. The derivation of such bounds involves only simple probabilistic and analytic tools. This complements the asymptotic expansions of Knessl (1998), Jacquet and Szpankowski (1999), and Flajolet (1999). The same method yields tight bounds on the relative entropy D(n, p) between a binomial and a Poisson, thus refining the work of Harremoës and Ruzankin (2004). Bounds on the entropy of the binomial also follow easily.