Distribution | Uniform (a, b) | Gamma (1, b) | Lomax (a, b) | Normal (m, v) |
---|---|---|---|---|
\( \frac{tVar(w)}{VaR(w)} \) | \( \frac{b\left(2-w\right)+ aw}{2\left(b\left(1-w\right)+ aw\right)} \) | \( 1-\frac{1}{ \log (w)} \) | \( \frac{a}{\alpha -1}; a>1 \) | \( m+\sqrt{v}\frac{\ {f}_{\tilde{c}}\left[VaR\left(1-w\right)\right]}{1-w} \) \( {f}_{\tilde{c}}\ is\ the\ Normal\ pdf \) |
f(w) : tVaR[w] = VaR[f(w)] | \( \frac{w}{2} \) | \( \frac{w}{e} \) | \( w{\left(\frac{a}{\alpha -1}\right)}^a \) | \( m+\sqrt{v}\left(1-{f}_{\tilde{c}}\left[VaR\left(1-w\right)\right]\right) \) |