Pareto Distribution Sample Generator
Enter the scale parameter \( x_m \), the shape parameter \(\alpha\), and the desired sample size \( n \). The generator uses inverse transform sampling: $$ x = \frac{x_m}{(1-u)^{1/\alpha}}, $$ where \( u \sim \text{Uniform}(0,1) \).
* Ensure \( x_m > 0 \), \(\alpha > 0\), and \( n \ge 1 \).
Step 1: Enter Parameters
e.g., 1
e.g., 2
e.g., 10
How It Works
The Pareto distribution sample is generated using the inverse CDF method: $$ x = \frac{x_m}{(1-u)^{1/\alpha}}, $$ where \( u \) is a uniformly distributed random number in \([0,1)\).
This method transforms uniformly distributed samples into samples from the Pareto distribution.