On the Entropy of Compound Distributions on Nonnegative Integers
On the Entropy of Compound Distributions on Nonnegative Integers
Some entropy comparison results are presented concerning compound distributions on nonnegative integers. The main result shows that, under a log-concavity assumption, two compound distributions are ordered in terms of Shannon entropy if both the ldquonumbers of claimsrdquo and the ldquoclaim sizesrdquo are ordered accordingly in the convex order. Several maximum/minimum …