Let X be any absolutely continuous random variable from the integrated
Pearson family and assume that X has finite moments of any order. Equivalently,
X is a linear (non-constant) transformation of Y where Y follows a Normal, a
Beta or a Gamma density. Using some properties of the orthonormal polynomial
system corresponding to X we provide a class of strengthened Chernoff-type
variance bounds. (A detailed review on orthogonal polynomials within the
Pearson system is included in the Appendix.)