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# Log-Normal Random Number Generator

The log-normal distribution is used to model situations in which the logarithm of a set of numbers fits a normal distribution. Although the parameters μ and σ appear in the PDF of the log-normal distribution, these are not the mean and standard deviation as they are in the normal distribution.

You can use the calculator below to generate a set of log-normally distributed random variables given values of μ and σ. The theoretical mean and variance are described below.

The probability density function of the log-normal distribution is

The mean, median, mode, variance, and skewness of the log-normal distribution are

mean = e^(μ + σ

^{2}/2)

median = e^(μ)

mode = e^(μ - σ

^{2})

variance = [e^(σ

^{2}) - 1]e^(2μ + σ

^{2})

skew = [e^(σ

^{2}) + 2]sqrt[e^(σ

^{2}) - 1]

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