Incident Severity Power-Law Ridge (3D)

Incident Dataset

Reports (n) 240

True tail exponent α 2.2

Embellishment bias 0.00

Fit Results

Fitted α (MLE)

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Log-log R²

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True α used

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Tail excess pts

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Verdict

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How it works

Every point here sits on a log-log floor: one axis is log(severity), the other is log(rank). A genuine power-law tail, P(x) ∝ x^−α, plots as a straight line in that space — so the ridge running across the floor is the least-squares fit, and each point's height is its residual off that ridge. Natural samples hover near the ridge; embellished reports get pushed upward, visibly bulging off the line the way an exaggerated retelling inflates a severity rating beyond what the natural decay predicts.

P(x) ∝ x^-α
log(rank) ≈ -α·log(severity) + C
α̂(MLE) = 1 + n / Σ ln(xᵢ/xmin)
height = residual = log(rank) - fit(log(severity))

Reports (n) — dataset size; more points make the ridge (or its distortion) clearer.
True tail exponent α — the exponent used to synthesize the "genuine" underlying reports.
Embellishment bias — the fraction of reports whose severity is artificially inflated by a retelling factor, bulging them off the ridge.

Drag to orbit the ridge. A flat, tight ridge with a high R² reads as natural power-law reporting; a bulging, scattered surface with poor fit is the statistical signature of embellished or fabricated severity claims.

Natural sample Embellished Fit ridge

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