### Log Normal Distribution

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The log normal distribution is often used when a set of measurements is badly skewed, but taking the logarithm of the measurements produces a distribution that is approximately normal. The log normal distribution has three parameters. The parameter a is the limiting value; no measurements will exist that are less than a. The parameter `mu` is the mean of the transformed (after logarithm) data. The parameter `sigma` is the standard deviation of the transformed data. The probability density and distribution functions are given by:

`f(x) = 1/((x-a)alpha(sqrt2pi))e^((-(log(x-a)-mu)^2)/(2sigma^2)`

`F(x) = Phi((log(x-a)-mu)/sigma)`