Distributions

Which shape do you actually want?

A distribution decides how likely each value is. Pick the one that matches what you're modelling — the difference between "any number" and "mostly middling numbers" is usually the whole point.

Uniform

Every value in the range is equally likely. The default, and the right answer more often than people expect.

Parameters

min — lowest possible value
max — highest possible value

Use it for

Dice rolls, lottery picks, raffle draws
Shuffling and random sampling
Anywhere you have no reason to prefer one value

Normal

The bell curve. Most values cluster near the mean, extremes are rare. About 68% land within one standard deviation.

Parameters

μ (mean) — where the curve is centred
σ (std deviation) — how wide the spread is

Use it for

Heights, test scores, measurement error
Monte Carlo simulation
Any natural quantity that averages out

Exponential

Small values are common, large ones increasingly rare — a steady decay. Models the waiting time until the next event.

Parameters

λ (lambda) — the rate; higher means faster decay

Use it for

Time between customer arrivals or server requests
Component lifetime before failure
Queue and reliability modelling

Poisson

Counts of things happening in a fixed window. Discrete by nature — you get whole numbers only.

Parameters

λ (lambda) — the average count per interval

Use it for

Support tickets per hour, goals per match
Defects per batch, calls per shift
Rare-event counting over time or space

Try one.

Change the distribution on the generator and watch the statistics move.

Start generating