Lognormal Distribution Calculator
Calculate P(X < x) for a lognormally distributed variable.
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Enter mu (mean of the underlying normal distribution of log values), sigma (standard deviation of log values), and x. The calculator computes P(X < x) by converting to a z-score: z = (ln(x) - mu) / sigma, then using the standard normal CDF.
About This Calculator
A variable has a lognormal distribution if its logarithm is normally distributed. The lognormal is always positive and right-skewed, making it ideal for modeling stock prices, income distributions, particle sizes, and other quantities that cannot be negative. Parameters mu and sigma refer to the underlying normal distribution, not the lognormal itself.
Frequently Asked Questions
What is the difference between mu/sigma and the actual mean/std dev?
Mu and sigma are parameters of the underlying normal distribution (of log values). The actual mean of the lognormal is exp(mu + sigma^2/2), which is higher than exp(mu).
What is the median of a lognormal distribution?
The median is exp(mu). This is always less than the mean due to the right skew.
When should I use the lognormal distribution?
Use it for data that is always positive, right-skewed, and where the log of the data appears normally distributed. Common examples: stock returns, city population sizes, enzyme concentrations.