Distributions
These distributions are available in the Probability Playground mini-language.
normal / norm
A symmetric bell-curve distribution.
x ~ norm(mean, std)
# or
x ~ normal(mean, std)
| Parameter | Description |
|---|---|
mean | Center of the distribution |
std | Standard deviation (spread) |
Example: revenue ~ norm(50000, 8000) — revenue centered around $50k with std of $8k.
uniform / unif
Every value in the range is equally likely.
x ~ uniform(low, high)
# or
x ~ unif(low, high)
| Parameter | Description |
|---|---|
low | Minimum value |
high | Maximum value |
Example: growth ~ uniform(0.02, 0.08) — growth rate uniformly between 2% and 8%.
triangular / tri
A three-point estimate — useful when you know a minimum, most likely, and maximum value.
x ~ triangular(low, mode, high)
# or
x ~ tri(low, mode, high)
| Parameter | Description |
|---|---|
low | Minimum value |
mode | Most likely value |
high | Maximum value |
Example: project_weeks ~ tri(4, 6, 12) — project takes 4–12 weeks, most likely 6.
lognormal / lognorm
A right-skewed distribution where values are always positive. Good for modeling costs, time, or quantities that can't be negative.
x ~ lognormal(mean, sigma)
# or
x ~ lognorm(mean, sigma)
| Parameter | Description |
|---|---|
mean | Mean of the underlying normal distribution (in log space) |
sigma | Standard deviation in log space |
exponential / expon
A memoryless distribution. Good for modeling waiting times.
x ~ exponential(rate)
# or
x ~ expon(rate)
| Parameter | Description |
|---|---|
rate | Rate parameter (mean = 1/rate) |
gamma
A flexible positive-value distribution. Generalizes the exponential.
x ~ gamma(shape, scale)
| Parameter | Description |
|---|---|
shape | Shape parameter (k) |
scale | Scale parameter (θ) |
beta
A distribution bounded between 0 and 1. Good for modeling probabilities, fractions, or proportions.
x ~ beta(alpha, beta)
| Parameter | Description |
|---|---|
alpha | Shape parameter α (> 0) |
beta | Shape parameter β (> 0) |
Example: conversion_rate ~ beta(2, 8) — conversion rate with most probability mass around 20%.
poisson
A discrete distribution for count data.
x ~ poisson(rate)
| Parameter | Description |
|---|---|
rate | Expected number of events (λ) |
Example: daily_signups ~ poisson(15) — average 15 signups per day.
Pr(x < X) line
After running a model, drag the vertical line on the histogram to read off the probability that the output variable is less than any given value. This is particularly useful for questions like:
- "What is the probability that profit is negative?" → drag to 0
- "What is the probability that this project finishes in under 10 weeks?" → drag to 10