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: $$ x = x_m \cdot 2^{\frac{1}{\alpha}}. $$