Distribution Transformation

If you take a random variable Y, and apply a function h(y) to every value is takes, the probability distribution will also be transformed.

Given a standard uniform distribution U (0 ≤ U ≤ 1), and transformation function h(u), the new random variable Y = h(U), has the distribution:

fY(y) = ddy h-1(y)

Using this tool, you can specify an equation to transform a standard uniform distribution. This is done by brute force computation for 100,000 random values. You can also specify an equation to graph over it, to see if you calculated the distribution equation correctly.

Transformation function h(y) =
Test function to graph t(y) =


My favorite is the transformation sqrt(y)

The new distribution is 2y, which is a triangle!


h(y) = sqrt(y)

h-1(y) = y2

fY(y) = ddy h-1(y) = ddy y2 = 2y