Definition of Log-Normal Distribution
The continuous random variable $X$ has a Log Normal Distribution if the random variable $Y=\ln (X)$ has a normal distribution with mean $\mu$ and standard deviation $\sigma$.
The probability density function of $X$ is \[ \begin{equation*} f(x;\mu,\sigma) =\left\{ \begin{array}{ll} \frac{1}{\sqrt{2\pi}\sigma x}e^{-\frac{1}{2\sigma^2}(\ln x -\mu)^2}, & \hbox{$x\geq 0$;} \\ 0, & \hbox{$x < 0$.} \end{array} \right. \end{equation*} \]
$\mu$is location parameter$\sigma$is scale parameter
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