log normal distribution
Assuming "log normal distribution" is a probability distribution | Use as instead

Input

log-normal distribution | normal mean | μ normal standard deviation | σ (positive)

Statistical properties

mean | e^(μ + σ^2/2) mode | e^(μ - σ^2) standard deviation | sqrt((e^(σ^2) - 1) e^(2 μ + σ^2)) variance | (e^(σ^2) - 1) e^(2 μ + σ^2) skewness | sqrt(e^(σ^2) - 1) (e^(σ^2) + 2)

Probability density function (PDF)

piecewise | e^(-(log(x) - μ)^2/(2 σ^2))/(sqrt(2 π) σ x) | x>0 0 | (otherwise)

Plots of PDF for typical parameters

Plots of PDF for typical parameters

Cumulative distribution function (CDF)

P (X<=x) = piecewise | 1/2 erfc((μ - log(x))/(sqrt(2) σ)) | x>0 0 | (otherwise)
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