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Uniform Difference Distribution

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UniformDifferenceDistribution

The difference X_1-X_2 of two uniform variates on the interval [0,1] can be found as

P_(X_1-X_2)(u)=int_0^1int_0^1delta((x-y)-u)dxdy
(1)
=1-u+2uH(-u),
(2)

where delta(x) is a delta function and H(x) is the Heaviside step function.

See also

Uniform Distribution, Uniform Product Distribution, Uniform Ratio Distribution, Uniform Sum Distribution

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Cite this as:

Weisstein, Eric W. "Uniform Difference Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UniformDifferenceDistribution.html

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