Binomial and Poisson distributions as maximum entropy distributions

The binomial and the Poisson distributions are shown to be maximum entropy distributions of suitably defined sets. Poisson's law is considered as a case of entropy maximization, and also convergence in information divergence is established.

[1]  Ingram Olkin,et al.  Entropy of the Sum of Independent Bernoulli Random Variables and of the Multinomial Distribution , 1981 .

[2]  L. L. Cam,et al.  Asymptotic methods in statistical theory , 1986 .

[3]  J. Steele.  Le Cam's inequality and poisson approximations , 1994 .

[4]  W. Ochs.  Basic properties of the generalized Boltzmann-Gibbs- Shannon entropy , 1976 .

[5]  L. L. Cam,et al.  An approximation theorem for the Poisson binomial distribution. , 1960 .

[6]  F. Topsøe.  Game Theoretical Equilibrium, Maximum Entropy and Minimum Information Discrimination , 1993 .

[7]  I. Csiszár.  $I$-Divergence Geometry of Probability Distributions and Minimization Problems , 1975 .

[8]  R. Serfling.  Some Elementary Results on Poisson Approximation in a Sequence of Bernoulli Trials , 1978 .

[9]  E. L. Presman.  Approximation in Variation of the Distribution of a Sum of Independent Bernoulli Variables with a Poisson Law , 1986 .

[10]  P. Deheuvels,et al.  A Semigroup Approach to Poisson Approximation , 1986 .

[11]  S. Y. Sorgin,et al.  Approximation of a Generalized Binomial Distribution , 1978 .

[12]  Flemming Topsøe,et al.  Information-theoretical optimization techniques , 1979, Kybernetika.

[13]  T. A. Azlarov,et al.  Refinements of Yu. V. Prokhorov's theorems on the asymptotic behavior of the binomial distribution , 1987 .

[14]  A. Barron.  ENTROPY AND THE CENTRAL LIMIT THEOREM , 1986 .

[15]  R. Serfling.  A General Poisson Approximation Theorem , 1975 .

[16]  Seiji Takano.  CONVERGENCE OF ENTROPY IN THE CENTRAL LIMIT THEOREM , 1987 .