Maximum variance unimodal distributions

John W. Seaman, Patrick S. Odell and Dean M. Young

Statistics & Probability Letters, 1985, vol. 3, issue 5, 255-260

Abstract: A new sufficient condition for the variance of a unimodal distribution in [left floor]a, b[right floor] to have the least upper bound (b - a)2/12 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 [left floor]a, b[right floor] is (b - a)2/9 is also given. These results are used to construct a new estimator of the variance of such distributions.

Keywords: bounds; inequalities; variance; estimation; unbiasedness (search for similar items in EconPapers)
Date: 1985
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