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Estimating Statistical Characteristics Under Interval Uncertainty And Constraints: Mean, Variance, Covariance, And Correlation, Ali Jalal-Kamali

Open Access Theses & Dissertations

In many practical situations, we have a sample of objects of a given type. When we measure the values of a certain quantity x for these objects, we get a sequence of values x1, . . . , xn. When the sample is large enough, then the arithmetic mean E of the values xi is a good approximation for the average value of this quantity for all the objects from this class. Other expressions provide a good approximation to statistical characteristics such as variance, covariance, and correlation.

The values xi come from measurements, and measurement is never absolutely accurate.

Often, …