Pareto Distribution Sample Generator

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.

Inverse CDF Formula: \( x = \frac{x_m}{(1-u)^{1/\alpha}} \)

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