customizedDistribution(piecewiseFunctions, desiredMin, desiredMax)
Overview
The function generates a random number based on custom piecewise functions within the desired range.
Parameters
| Parameter | Type | Description |
|---|---|---|
piecewiseFunctions |
Table | A table containing subtables, each with a function string, x_{\text{min}} , and x_{\text{max}} for each piecewise function. |
desiredMin |
Number | The minimum desired value of the scaled random number. |
desiredMax |
Number | The maximum desired value of the scaled random number. |
Returns
| Return | Type | Description |
|---|---|---|
randomX |
Number | A scaled random number in the range [desiredMin, desiredMax]. |
Example
local functions = {{"x^2", 0, 2}, {"2*x", 2, 4}}
local randomX = StatBook.customizedDistribution(functions, 0, 10)
print(randomX) -- Output will vary
Mathematical Background
The function employs a Monte Carlo method using the custom piecewise functions provided. It randomly selects one of the piecewise functions and generates a random coordinate (\text{randomX}, \text{randomY}) within its range and below its absolute maximum value. The function value at this \text{randomX} is calculated using the user-provided function, and the coordinate is accepted if \text{randomY} \leq \text{number}. The accepted \text{randomX} value is then scaled to fall within [desiredMin, desiredMax].
\text{randomX} = \text{desiredMin} + \left( \text{randomX} - x_{\text{min}} \right) \times \frac{\text{desiredMax} - \text{desiredMin}}{x_{\text{max}} - x_{\text{min}}}