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
Log-Normal Probability Calculator
First Parameter ($\mu$)
Second parameter ($\sigma$)
P(X< A)
P(X > B)
P(A< X < B) and
Outside A and B and
Mean :
Variance :
Required Probability :

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