A new transformation of continuous unimodal asymmetric probability distributions into possibility distributions

Abstract This paper deals with a new transformation, so-called two-sided normalized (TSN), of continuous unimodal asymmetric probability distributions into possibility distributions. Many properties are derived and interpretations are discussed. A comparison with the optimal transformation is provided. In particular, the respective positions of right or left branches relative to the resulting optimal and TSN possibility distributions are given. It is also shown that the TSN transformation is the optimal transformation for the particular family of two-piece skewed distributions. The preservation of the asymmetry property is then analyzed and illustrated for several conventional asymmetric distributions and counter-examples of asymmetry preservation are provided. A multilinear approximation of the TSN transformation is finally proposed.

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