吉尔布拉特分布¶
对数正态的特例 \(\sigma=1\) 和 \(S=1.0\) ，通常还会 \(L=0.0\) 。)
\BEGIN{等式*}f\Left(x；\sigma\Right)&=&\frac{1}{x\sqrt{2\pi}}\exp\left(-\frac{1}{2}\left(\log x\Right)^{2}\Right)\\
F\Left(x；\sigma\Right)&=&\Phi\Left(\log x\right)=\frac{1}{2}\left(1+\mathrm{erf}\left(\frac{\log x}{\sqrt{2}}\Right)\Right)\\
g\Left(q；\sigma\Right)&=&\exp\Left(\phi^{-1}\Left(Q\Right)\Right)\end{eqnarray*}
\BEGIN{eqnarray*}\mu&=&\sqrt{e}\\
\MU_{2}&=&e\Left [e-1\right] \\
\Gamma_{1}&=&\sqrt{e-1}\Left(2+e\Right)\\
\Gamma_{2}&=&e^{4}+2e^{3}+3e^{2}-6\end{eqnarray*}
\BEGIN{eqnarray*}h\Left [X\right] &=&\log\Left(\sqrt{2\pi e}\Right)\\
&\约&1.4189385332046727418\end{eqnarray*}