generateLogNormal(mu, sigma)
Overview
The generateLogNormal(mu, sigma) function generates a random number that follows a log-normal distribution.
Parameters
| Parameter | Type | Description |
|---|---|---|
mu |
Number | The mean parameter of the underlying normal distribution. |
sigma |
Number | The standard deviation parameter of the underlying normal distribution. |
Returns
| Return | Type | Description |
|---|---|---|
result |
Number | A random number from a log-normal distribution. |
Example
local result = StatBook.generateLogNormal(0, 1)
print(result) -- Output will vary
Mathematical Background
The function generates a random number result that follows a log-normal distribution with parameters \mu and \sigma . A log-normal distribution is useful in various applications, including finance and ecology, where the values must be positive.
To generate result , the function uses the Box-Muller method to generate a standard normally distributed random variable Z . The function then calculates result using:
result = \exp(\mu + \sigma \times Z)