Strengthened Chernoff-type variance bounds

Details Strengthened Chernoff-type variance bounds Strengthened Chernoff-type variance bounds

2011-07-09

arxiv.org/abs/1107.1754v1

Statistics

Methodology

14 pages + 28 pages a review APPENDIX on Pearson family. Total 42 pages

Scientific paper

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.)

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