Pareto Distribution Mode Calculator
Enter the scale parameter \( x_m \) and the shape parameter \(\alpha\) to calculate the mode of the Pareto distribution.
* Note: The mode of the Pareto distribution is always equal to the scale parameter \( x_m \), regardless of \(\alpha\).
Step 1: Enter Parameters
e.g., 1
e.g., 2 (Note: This value does not affect the mode)
How It Works
The PDF of the Pareto distribution is given by: $$ f(x) = \frac{\alpha x_m^\alpha}{x^{\alpha+1}}, \quad x \ge x_m. $$
Since the PDF is a strictly decreasing function for \( x \ge x_m \), the maximum value (mode) occurs at \( x = x_m \). Thus, the mode is: $$ \text{Mode} = x_m. $$