Some Elementary Variations of the Lyapunov Inequality
Barry C. Arnold · SIAM Journal on Applied Mathematics · 1978
A moment inequality derived by Petrov [1] is shown to follow from the classical Lyapunov inequality applied to a certain conditional distribution. A general conditional version of the Lyapunov inequality is presented. The performance of the Petrov inequality is compared with that of a related tighter inequality (also obtained by conditioning) in the case of a geometrically distributed random variable.