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Upper bounds for the variances of certain random variables |
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| Authors: | S. W. Dharmadhikari Kumar Joag - Dev |
| Affiliation: | 1. Department of Mathematics , Southern Illinois University , Carbondale, IL 62901;2. Department of Statistics , University of Illinois , 725 S. Wright Street, Champaign, IL 61820 |
| 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 |