Lognormal Distribution Random Generator
Generate random numbers from a lognormal distribution. Enter the parameters mu and sigma and a count, then click to produce a sample list, histogram, and sample mean and median.
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Input
Enter the lognormal parameters mu and sigma and the number of values, then press the generate button to create random numbers.
log mean
log SD
values
Enter a value from 1 to 5000.
Result
Enter the parameters and count, then press the generate button.
How it works
- The lognormal distribution is the distribution of positive values whose logarithm follows a normal distribution N(mu, sigma^2). If Z is a standard normal random number, then X = exp(mu + sigma * Z) follows the lognormal distribution with parameters (mu, sigma).
- This tool first draws a standard normal value Z with the Box-Muller method, then computes X = exp(mu + sigma * Z) to produce each lognormal value. Random numbers are generated only when you press the button.
- The theoretical mean is exp(mu + sigma^2 / 2) and the theoretical median is exp(mu). You can compare these with the sample mean and median of the generated values.
- Sigma must be positive and the count must be between 1 and 5000. The larger the count, the closer the histogram gets to the shape of the theoretical distribution.
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