Maximum variance unimodal distributions |
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Authors: | John W Seaman Patrick S Odell Dean M Young |
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Affiliation: | Baylor University, Waco, TX 76798, USA;University of Texas at Dallas, Richardson, TX 75080, USA;Baylor University, Waco, TX 76798, USA |
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Abstract: | A new sufficient condition for the variance of a unimodal distribution in ?a, b? to have the least upper bound is derived. This condition is more general than the condition found by Jacobson (1969). A new proof that the least upper bound for all unimodal distributions in ?a, b? is is also given. These results are used to construct a new estimator of the variance of such distributions. |
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Keywords: | bounds inequalities variance estimation unbiasedness |
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