# How to calculate the distortion function for EVaR?

As defined in Entropic Value-at-Risk: A New Coherent Risk Measure (reference) by A.Ahmadi-Javid, the entropic value-at-risk (EVaR) of $x\in L_{M^{+}}$ with confidence level $1-\alpha$ is: $$EVaR_{1-\alpha}(X) := \inf_{z>0}\left\{z^{-1}\ln\left(\frac{M_{X}}{\alpha}\right)\right\}$$ where $M_X$ is the moment generating function.

I was wondering can EVaR fit in the framework of distortion risk measures? And in that case how to calculate the distortion function for EVaR?