论文信息 - Entropy of the Sum of Independent Bernoulli Random Variables and of the Multinomial Distribution

Entropy of the Sum of Independent Bernoulli Random Variables and of the Multinomial Distribution

ABSTRACT For sums of independent Bernoulli random variables and for the multinomial distribution it is shown that the entropy h gives a measure of the degree of uniformness of the distribution π, that is, the larger h is, the more uniform is π. The method of proof is based on showing that the entropy function is Schur convex.

Ingram Olkin | L. A. Shepp

[1] W. Hoeffding. On the Distribution of the Number of Successes in Independent Trials , 1956 .

[2] Yossef Rinott. Multivariate majorization and rearrangement inequalities with some applications to probability and statistics , 1973 .

[3] P. Mateev. On the Entropy of the Multinomial Distribution , 1978 .

[4] L. Gleser. On the Distribution of the Number of Successes in Independent Trials , 1975 .

[5] Ingram Olkin,et al. Majorization in Multivariate Distributions , 1974 .