generateStandardNormal()
Overview
The generateStandardNormal() function generates a random number that follows a standard normal distribution using the Box-Muller transform.
Parameters
No parameters are required.
Returns
| Return | Type | Description |
|---|---|---|
x |
Number | A random number from a standard normal distribution. |
Example
local x = StatBook.generateStandardNormal()
print(x) -- Output will vary
Mathematical Background
The function internally utilizes the Box-Muller transform to generate a random number x that follows a standard normal distribution. This distribution has a mean of 0 and a standard deviation of 1.
The Box-Muller transform generates two independent standard normally distributed normal variables, Z_0 and Z_1 , from two uniformly distributed random variables U_1 and U_2 .
Z_0 = \sqrt{-2 \ln(U_1)} \cos(2\pi U_2)
Z_1 = \sqrt{-2 \ln(U_1)} \sin(2\pi U_2)
In this function, either Z_0 or Z_1 is returned as x .