Advances and Applications in Statistics
Volume 47, Issue 3, Pages 211 - 224
(December 2015) http://dx.doi.org/10.17654/ADASDec2015_211_224 |
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BOUNDS ON VARIANCE BASED ON DIFFERENCES OF MASS POINTS
Kamal Samy Selim
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Abstract: Given a random sample drawn with replacement from a discrete distribution and arranged as a probability mass function, sharp bounds on the sample variance are obtained in terms of the mass points differences and the masses. Under the assumption that the sample observations are pairwise uncorrelated, and jointly distributed with common mean and variance, lower bounds on the population variance are also obtained as functions of the expected differences of mass points. The new bounds extend some well known results in the literature, and expand their theoretical and practical applications. |
Keywords and phrases: variance inequality, difference of order statistics, sample range, discrete random variable, Cauchy-Schwarz inequality. |
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