Year: 2019
Type: article
Abstract: Consider tossing a collection of coins, each fair or biased towards heads, and take the distribution of the total number of heads that result. It is natural to suppose that this distribution should be ‘more random’ when each coin is fairer. In this paper, we prove a 40 year old conjecture of Shepp and Olkin, by showing that the Shannon entropy is monotonically increasing in this case, using a construction inspired by optimal transport theory. We discuss whether this result can be generalized to $q$-Rényi and $q$-Tsallis entropies, for a range of values of $q$.
DOI: 10.1214/19-ejp380
Authors: Erwan Hillion, Oliver Johnson
Institutions: Aix-Marseille Université, University of Bristol
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W2897736899