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Why 95% And Two Sigma? A Theoretical Justification For An Empirical Measurement Practice, Hung T. Nguyen, Vladik Kreinovich, Chin-Wang Tao
Why 95% And Two Sigma? A Theoretical Justification For An Empirical Measurement Practice, Hung T. Nguyen, Vladik Kreinovich, Chin-Wang Tao
Departmental Technical Reports (CS)
The probability p(k) that the value of a random variable is far away from the mean (e.g. further than k standard deviations away) is so small that this possibility can be often safely ignored. It is desirable to select k for which the dependence of the probability p(k) on the distribution is the smallest possible. Empirically, this dependence is the smallest for k between 1.5 and 2.5. In this paper, we give a theoretical explanation for this empirical result.