DISTRIBUTIONSSTARTER

Power Law / Long Tail

Rich-get-richer: a few huge winners, many tiny players. Straight line on log-log.

log–log: straight line · recreated schematic

How it works

Growth plus preference for the already-big compounds into extremes.
On log-log axes the curve straightens — slope is the exponent.
The mean misleads: most sit below it, a few tower above.

Use → City sizes, book sales, network degrees. Never average it like a normal.

Watch out → Averaging power-law data invents a 'typical' case that barely exists.

Try it → Rank site traffic or sales by size and plot rank vs size on log-log.

REDCAPE jobs → Explain · Predict

Free sources → SFI Fractals & Scaling • Wikipedia: Power law (CC BY-SA)

◍ Mentor soonSee REDCAPE playbook →

Attach to a lattice — combines with

Different families, shared jobs. Disagreement between them is where insight lives.

Exponential & Solow Growth

Compounding plus capital, labor and ideas explain why some economies stall.

SHARED JOBS: EXPLAIN · PREDICT

SORTING & PEER EFFECTS

Granovetter Threshold

Each person has a join threshold; cascades depend on the distribution, not the average.

SHARED JOBS: EXPLAIN · PREDICT

Percolation / Tipping Points

Sparse links suddenly gel into a giant component — bank networks and blackouts tip fast.

SHARED JOBS: EXPLAIN · PREDICT

More in Distributions

Normal Distribution

Bell-curve averaging: many small independent effects sum to a predictable center with thin tails.

Central Limit & Six Sigma

Sample averages settle to normal; variation reduction pays until returns diminish.

Poisson Arrivals

Counts of rare independent events per window: calls, mutations, clicks.

← Central Limit & Six Sigma Poisson Arrivals →