\begin{eqnarray*}
    f\left(x;c\right) & = & \left\{
                                \begin{array}{ccc}
                                    \frac{c}{2}x^{c-1} &  & 0 < x < 1 \\
                                    \frac{c}{2}x^{-c-1} &  & x \geq 1
                                \end{array}
                            \right. \\
    F\left(x;c\right) & = & \left\{
                                \begin{array}{ccc}
                                    \frac{1}{2}x^{c} &  & 0 < x < 1 \\
                                    1-\frac{1}{2}x^{-c} &  & x \geq 1
                                \end{array}
                            \right. \\
    G\left(q;c\right) & = & \left\{
                                \begin{array}{ccc}
                                    \left(2q\right)^{1/c} &  & 0 \leq q < \frac{1}{2} \\
                                    \left(2-2q\right)^{-1/c} &  & \frac{1}{2} \leq q \leq 1
                                \end{array}
                            \right.
\end{eqnarray*}

 h\left[X\right]=\log\left(\frac{2e}{c}\right)