Pareto Distribution Mode Calculator

Pareto Distribution Mode Calculator

Enter the scale parameter xm and the shape parameter α to calculate the mode of the Pareto distribution.

* Note: The mode of the Pareto distribution is always equal to the scale parameter xm, regardless of α.

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)=αxmαxα+1,xxm.

Since the PDF is a strictly decreasing function for xxm, the maximum value (mode) occurs at x=xm. Thus, the mode is: Mode=xm.

Formula: Mode=xm

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