# Log-Normal Distribution > A lognormal distribution is a continuous distribution of a RV whose *logarithm* is normally distributed. #### Probability Density Function A positive random variable $X$ is log-normally distributed (i.e., $X \sim Lognormal(\mu_x, \sigma_x^2)$) if the natural logarithm of $X$ is normally distributed with mean $\mu$ and variance $\sigma^2$: $ln(X) \sim \mathcal{N}(\mu, \sigma^2)$ #### Generation Let $Z$ be a standard normal variable and let $\mu$ and $\sigma > 0$ be two real numbers. Then, the distribution of the random variable: $X = e^{\mu + \sigma Z}$ is called the log-normal distribution.  --- Date: 20220713 Links to: Tags: #review References: * [Log-normal distribution - Wikipedia](https://en.wikipedia.org/wiki/Log-normal_distribution)