Data transformations when constructing a composite system quality index

Abstract

Abstract The features of the data distribution can significantly affect the composite characteristics of objects, so composite indexes of objects must necessarily take into account the features of the data. Some types of data are characterized by distributions with a significant anomaly, when the vast majority of observations are concentrated near the boundary values. This type of data cannot always be characterized by an asymmetry coefficient. In addition, if the values of a variable are approximately symmetric with respect to zero or are concentrated near zero, the sample cannot also be characterized by the coefficient of variation. The paper proposes a transformation that allows us to identify the anomalous nature of variables using the signal-to-noise ratio. Variables are evaluated in the standard range, which is shifted to the right relative to zero. If it is necessary to logarithm, such a transformation will avoid the pressure of small values of variables that, after direct logarithm, would have large negative values. The application of logarithmic correction for the detected anomalous variables redistributes the values of the obtained weighting coefficients in the direction of a more correct interpretation and, in particular, solves the problem with the negativity of the weighting coefficients.