Upper bounds for the variances of certain random variables

Abstract

Jacobson (1969) proved that the variance of a unimodal distribution on the unit interval is bounded above by 1/9. This paper generalizes Jacobson's result by deriving sharp upper bounds for the variances of α-unimodal distributions and for the variances of S-shaped distributions.

Keywords:

• Unimodality
• Variance bounds
• S-Shaped Distributions