Unified extension of variance bounds for integrated Pearson family

Abstract

We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds are better than the existing ones.

14 pages

References in corpus (2)

• An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds
• Strengthened Chernoff-type variance bounds

Cited by in corpus (2)

• Orthogonal polynomials in the Cumulative Ord family and its application to variance bounds
• A note on a variance bound for the multinomial and the negative multinomial distribution