Mildenhall Aggregate

Loss Tools

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Example 3: Step-by-Step Convolution: Inputs

X Distribution 0 0.5 0.5 0 0 0 0 0	Y Distribution 0 0 1 0 0 0 0 0

Click compute to see results...

Notes

Uniform(4) distribution gives equal probability to losses of 0, 1, 2 or 3.
The sum of two Uniform(4) distributions is a triangular distribution.
Add One: sets Y distribution to the degenerate distribution with Pr(Y=1) = 1. This shifts the X distribution down by one.

References to Wang

Section 2.3
Section 2.3.3 exactly describes this example.