Transmuted Distortion Functions for Measuring Risks

This paper introduces a new family of distortion functions for measuring risks, developed using transmutation techniques. We identify the parameter spaces where the proposed distortions exhibit concavity. Considering that the choice of distortion parameters can be influenced by political factors or users’ risk aversion levels, we generate plots of the distortion functions to examine how these parameters impact the tasks and users’ attitudes toward risk. The coherent properties of the resulting risk measures are explored, outlining the conditions under which the transmuted Kumaraswamy and transmuted truncated normal distortions ensure coherence. Numerical analyses demonstrate the effects of parameter variations on the derived risk measures, highlighting the effectiveness of the proposed distortion functions in accurately assessing risk.