Fano’s Inequality for Random Variables

Fano's inequality for random variables

We extend Fano’s inequality, which controls the average probability of (disjoint) events in terms of the average of some Kullback-Leibler divergences, to work with arbitrary [0, 1]–valued random variables. Our simple two-step methodology is general enough to cover the case of an arbitrary (possibly continuously infinite) family of distributions as well as [0, 1]–valued random variables not nece...

An entropy inequality for symmetric random variables

We establish a lower bound on the entropy of weighted sums of (possibly dependent) random variables (X1, X2, . . . , Xn) possessing a symmetric joint distribution. Our lower bound is in terms of the joint entropy of (X1, X2, . . . , Xn). We show that for n ≥ 3, the lower bound is tight if and only if Xi’s are i.i.d. Gaussian random variables. For n = 2 there are numerous other cases of equality...

Recurring Mean Inequality of Random Variables

The theory of means and their inequalities is fundamental to many fields including mathematics, statistics, physics, and economics.This is certainly true in the area of probability and statistics. There are large amounts of work available in the literature. For example, some useful results have been given by Shaked and Tong 1 , Shaked and Shanthikumar 2 , Shaked et al. 3 , and Tong 4, 5 . Motiv...

An Exponential Inequality for Negatively Associated Random Variables

An exponential inequality is established for identically distributed negatively associated random variables which have the finite Laplace transforms. The inequality improves the results of Kim and Kim 2007 , Nooghabi and Azarnoosh 2009 , and Xing et al. 2009 . We also obtain the convergence rate O 1 n1/2 logn −1/2 for the strong law of large numbers, which improves the corresponding ones of Kim...

Dominated Convergence for Fuzzy Random Variables