The noise distribution and its tail
Chart. Use the left and right arrow keys to move along the noise values, the up and down arrow keys or Shift with an arrow to move ten at a time, Home and End for the ends; Escape hides the reading.
The centre is a poor guide to the tail.
The largest variance component is bounded. Replacing it with a Gaussian adds tail mass that the exact law does not have.
Chart data
Where the variance comes from
Variances rounded for display. Shape sketches use independent horizontal scales.
Four ways to price the tail
Estimate a tail too rare to observe
Exponential tilting puts draws in the tail, then corrects their weights.
Chernoff optimum
The standard error describes simulation noise, not uncertainty in the noise model.
Chart. Use the left and right arrow keys to move between recorded batches, Home and End for the first and latest; Escape hides the reading.
Draws · same seed and parameters throughout
Building the distribution
The same operation that adds claim amounts can add coefficient noise.
What if
Positive Δ means a higher failure bound. Custom results change one parameter at a time from the selected baseline. Only the three FIPS 203 sets are standardised.
From coefficient noise to a failure bound
The threshold convention and the modelling assumptions remain part of the result.