Uncertainty and models

Probability-probability plot (PP plot)

Compares cumulative probabilities under two distributions to assess agreement.

What it answers

Do cumulative probabilities agree across distributions?

The question

Does our fitted model of call lengths match the observed calls?

Points sit slightly above the diagonal in the middle range: the model expects a little fewer short calls than were seen. Elsewhere the fit is close.

Illustrative data. It belongs to no company.

Assessing distributional agreement, especially central probabilities.

When tail differences are the main interest or probabilities are misaligned.

Compare probability pairs with the diagonal.

Specify the compared distributions or fitted model.

Layout: Paired probability table
Fields: ProbabilityA: number; ProbabilityB: number
One row is: One pair of cumulative probabilities at a common evaluation point. What is the grain?
Rules: Both probabilities must be within [0,1]. Explain the distributions and common evaluation points.
Optional: Raw alternative: observations plus two specified CDFs or a fitted comparison model.
Preparation: Compute paired CDF probabilities at common evaluation points and retain the fitted-distribution specification.
Units: Both axes are cumulative probabilities in[0,1], based on stated distributions.

A long table: one row per observation, few columns. New data adds rows.

Pairs(0.1,0.08),(0.5,0.55),(0.9,0.94). Compare with Y=X. The middle pair is 0.05 above the diagonal.