# Dictionary:Laplacian distribution

${\displaystyle f(x)={\frac {1}{\sigma }}e^{-{\frac {|x-\mu |}{\sigma }}}}$
where ${\textstyle \mu }$ locates the mode of the distribution curve and ${\textstyle \sigma }$ is a shape parameter. The maximum likelihood is the median for independent random variables. Yields a normal distribution when the median equals the mean. See Johnson and Kutz (1969, 22).