Special cases
A broad family collapses to a familiar one at a particular parameter value. Exponential is Weibull with shape 1; chi-square is gamma with shape k/2 and scale 2. These are identities, not approximations.
Reference / The relationship map
Don’t memorize the catalog.
Learn the moves.
The original chart encodes hundreds of links. This guided view starts with its central backbone—the relationships that recur constantly in statistics and machine learning.
How to read thisArrow direction follows the construction or convergence. Hover an edge for its mathematical statement; filter by relationship type above.
Transformations
A deterministic operation on random variables produces another law. Standardizing a normal gives a standard normal; squaring and summing standard normals gives chi-square; applying a quantile function to a uniform variate creates a sample.
Limiting results
A sequence of models approaches another distribution. Sparse binomial counts become Poisson, large Poisson counts become normal, and Student t becomes normal as its degrees of freedom grow.
Bayesian relationships
A prior and likelihood share an algebraic shape, so updating preserves the family. A Beta prior paired with Bernoulli or binomial data yields a Beta posterior by simply adding counts.
All 76 distributions
without losing your place.
Explore the source
without losing your place.
Pan, zoom, search, and select every distribution on the original chart. Foundational nodes jump directly into the computational playground.
Drag to pan · select a box for details
Interactive source chart
Every distribution box in the original chart is selectable. Relationship arrows retain their original mathematical labels.
Open text index →The source in full
76 distributions.
Far more than 76 ideas.
The guided graph intentionally reduces visual density. Use the original Leemis–McQueston diagram below as the comprehensive reference; zoom to inspect formula labels and property marks.
Read provenance and notation →