General relative entropy inequality: an illustration on growth models

General relative entropy inequality: an illustration on growth models

We introduce the notion of General Relative Entropy Inequality for several linear PDEs. This concept extends to equations that are not concervation laws, the notion of relative entropy for conservative parabolic, hyperbolic or integral equations. These are particularly natural in the context of biological applications where birth and death can be described by zeroth order terms. But the concept...

Measuring inequality: tools and an illustration

BACKGROUND This paper examines an aspect of the problem of measuring inequality in health services. The measures that are commonly applied can be misleading because such measures obscure the difficulty in obtaining a complete ranking of distributions. The nature of the social welfare function underlying these measures is important. The overall object is to demonstrate that varying implications ...

An Illustration of Second-Order Latent Growth Models

A general minimax result for relative entropy

Suppose Nature picks a probability measure P on a complete separable metric space X at random from a measurable set P fP g Then without knowing a statistician picks a measure Q on X Finally the statistician su ers a loss D P jjQ the relative entropy between P and Q We show that the minimax and maximin values of this game are always equal and there is always a minimax strategy in the closure of ...

A note on inequalities for Tsallis relative operator entropy

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...