A New Entropy Power Inequality for Integer-Valued Random Variables
نویسندگان
چکیده
منابع مشابه
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...
متن کاملStable Poisson Convergence for Integer-valued Random Variables
Abstract. In this paper, we obtain some stable Poisson Convergence Theorems for arrays of integer-valued dependent random variables. We prove that the limiting distribution is a mixture of Poisson distribution when the conditional second moments on a given σ-algebra of the sequence converge to some positive random variable. Moreover, we apply the main results to the indicator functions of rowis...
متن کاملCompound Poisson process approximation for locally dependent real valued random variables via a new coupling inequality
In this work we present a general and quite simple upper bound for the total variation distance dTV between any stochastic process (Xi)i2 de ned over a countable space , and a compound Poisson process on : This result is su¢ cient for proving weak convergence for any functional of the process (Xi)i2 when the real valued Xis are rarely nonzero and locally dependent. Our result is being establis...
متن کاملA reverse entropy power inequality for log-concave random vectors
We prove that the exponent of the entropy of one dimensional projections of a log-concave random vector defines a 1/5-seminorm. We make two conjectures concerning reverse entropy power inequalities in the log-concave setting and discuss some examples. 2010 Mathematics Subject Classification. Primary 94A17; Secondary 52A40, 60E15.
متن کاملFano'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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2014
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2014.2317181