V.: Estimating Correlation under Interval Uncertainty

In many engineering situations, we are interested in finding the corre-lation between different quantities x and y based on the values xi and yi of these quantities measured in different situations i. Measurements are never absolutely accurate; it is therefore necessary to take this inaccu-racy into account when estimating the correlation . Sometimes, we know the probabilities of different values of measurement errors, but in many cases, we only know the upper bounds ∆xi and ∆yi on the corresponding measurement errors. In such situations, after we get the measurement results exi and eyi, the only information that we have about the actual (unknown) values xi and yi is that they belong to the corresponding in-tervals [exi ∆xi;exi +∆xi] and [eyi ∆yi; eyi +∆yi]. Different values from these intervals lead, in general, to different values of the correlation . It is therefore desirable to find the range [; ] of possible values of the correlation when xi and yi take values from the corresponding intervals