generateNormal(mu, sigma)
Overview
The generateNormal function generates a random number following a normal distribution characterized by a given mean (mu) and standard deviation (sigma).
Parameters
| Parameter | Type | Description | Default |
|---|---|---|---|
mu |
Number | The mean of the normal distribution. | - |
sigma |
Number | The standard deviation of the normal distribution. | - |
Returns
| Return | Type | Description |
|---|---|---|
x |
Number | A random number following the specified normal distribution. |
Example
local mu = 0
local sigma = 1
local randomNum = StatBook.generateNormal(mu, sigma)
print(randomNum) -- Output will vary based on random generation
Mathematical Background
The function uses the Box-Muller transform to generate a normally distributed random number x , given a mean \mu and standard deviation \sigma .
Given two independent and uniformly distributed random numbers U_1 and U_2 , the Box-Muller transform generates a standard normally distributed random variable Z :
Z = \sqrt{-2 \ln(U_1)} \cos(2\pi U_2)
To adapt this to a general normal distribution with mean \mu and standard deviation \sigma , the function performs the following transformation:
x = \mu + \sigma \times Z