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Article

Transmuted Distortion Functions for Measuring Risks

by
Muna Alkasasbeh
*,
Carl Lee
and
Felix Famoye
Department of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USA
*
Author to whom correspondence should be addressed.
Risks 2024, 12(10), 153; https://doi.org/10.3390/risks12100153
Submission received: 14 August 2024 / Revised: 10 September 2024 / Accepted: 23 September 2024 / Published: 26 September 2024

Abstract

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.
Keywords: transmuted distortion function; coherent risk measure; transmuted Kumaraswamy distortion; transmuted truncated normal distortion transmuted distortion function; coherent risk measure; transmuted Kumaraswamy distortion; transmuted truncated normal distortion

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MDPI and ACS Style

Alkasasbeh, M.; Lee, C.; Famoye, F. Transmuted Distortion Functions for Measuring Risks. Risks 2024, 12, 153. https://doi.org/10.3390/risks12100153

AMA Style

Alkasasbeh M, Lee C, Famoye F. Transmuted Distortion Functions for Measuring Risks. Risks. 2024; 12(10):153. https://doi.org/10.3390/risks12100153

Chicago/Turabian Style

Alkasasbeh, Muna, Carl Lee, and Felix Famoye. 2024. "Transmuted Distortion Functions for Measuring Risks" Risks 12, no. 10: 153. https://doi.org/10.3390/risks12100153

APA Style

Alkasasbeh, M., Lee, C., & Famoye, F. (2024). Transmuted Distortion Functions for Measuring Risks. Risks, 12(10), 153. https://doi.org/10.3390/risks12100153

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