Pareto Distribution Median Calculator

Pareto Distribution Median Calculator

Enter the scale parameter \( x_m \) and the shape parameter \(\alpha\) to calculate the median of the Pareto distribution.

* Ensure \( x_m > 0 \) and \(\alpha > 0\).

Step 1: Enter Parameters

e.g., 1

e.g., 2

How It Works

For a Pareto distribution, the median is the value at which the cumulative distribution function (CDF) is 0.5. The CDF is given by: $$ F(x) = 1 – \Bigl(\frac{x_m}{x}\Bigr)^\alpha, \quad x \ge x_m. $$

Setting \( F(x) = 0.5 \) and solving for \( x \) yields: $$ x = x_m \cdot 2^{\frac{1}{\alpha}}. $$

Formula: \( \text{Median} = x_m \cdot 2^{\frac{1}{\alpha}} \)

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