generatePareto(alpha, xm)
Overview
The generatePareto(alpha, xm) function generates a random number that follows a Pareto distribution with shape parameter alpha and scale parameter xm.
Parameters
| Parameter | Type | Description |
|---|---|---|
alpha |
Number | The shape parameter for the Pareto distribution. |
xm |
Number | The scale parameter for the Pareto distribution. |
Returns
| Return | Type | Description |
|---|---|---|
result |
Number | A random number from a Pareto distribution. |
Example
local result = StatBook.generatePareto(2, 1)
print(result) -- Output will vary
Mathematical Background
The function generates a random number result that follows a Pareto distribution with shape parameter \alpha and scale parameter xm .
The probability density function (pdf) for the Pareto distribution is:
f(x; \alpha, xm) = \alpha xm^\alpha x^{-(\alpha + 1)} \quad \text{for } x \geq xm, \alpha > 0
In this implementation, the Pareto distribution is generated using the formula:
\text{result} = xm \times (1 - \text{random})^{-\frac{1}{\alpha}}