ComposedDistributions

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A verb grammar for n-ary composition over any Distributions.jl distribution.

Why ComposedDistributions?

• Compose delays into chains (sequential), independent branches (parallel), fixed-probability or racing one_of outcomes (resolve / compete) and data-selected disjunctions (choose), over any UnivariateDistribution.
• One object scores an observed record with logpdf and simulates one with rand, so a model is built once and used in both directions.
• Build a whole tree from a NamedTuple, a Tables.jl table, or a nested matrix with compose, and read its structure with params_table, event_names, event, and event_tree.
• Turn the parameter table into a nested prior with build_priors, and edit the tree with update, prune, and splice.
• Attach parameter uncertainty with uncertain (parameters that are themselves distributions, nestable): rand draws the marginal, and update(tree, params) collapses an uncertain leaf to its concrete template.
• Hard-deps and re-exports ConvolvedDistributions (a chain collapses to a convolved total via observed_distribution), so its convolution and quadrature surface is reachable through this package alone.
• No censoring: this is the generic composition layer.

Getting started

See documentation for a full walkthrough.

using ComposedDistributions, Distributions

# A two-step delay chain, then its parameter table and a default prior set.
tree = compose((onset_admit = [Gamma(2.0, 1.0), LogNormal(0.5, 0.4)],))
params_table(tree)
priors = build_priors(params_table(tree))

# A death-vs-discharge competition (the death branch probability is the CFR).
node = resolve(:death => (Gamma(1.5, 1.0), 0.3), :disch => Gamma(2.0, 1.5))
mean(node)

Relationship to Distributions.jl

ComposedDistributions builds on Distributions.jl rather than replacing it. Every leaf is a Distributions.jl UnivariateDistribution, and a composed object is itself a Distribution, so logpdf, rand, mean, var and the rest of the interface work unchanged.

Aspect	Distributions.jl	ComposedDistributions
Scope	one distribution	many delays wired into an event tree
Question	"what is this delay?"	"how do these events relate?"
Builds on	—	any Distributions.jl UnivariateDistribution as a leaf
Adds	—	compose, the five composers, a parameter table and structural edits

Because a composed object is a Distribution, it also works with truncated() from Distributions.jl and drops into any code that expects a distribution.

What packages work well with ComposedDistributions?

• Distributions.jl supplies the leaf distributions and the interface a composed object implements.
• ConvolvedDistributions.jl is re-exported, so convolution (convolve_distributions, difference) and quadrature are reachable through ComposedDistributions alone.
• Tables.jl sources build a composer through compose, and params_table returns a Tables.jl table.
• Turing.jl and the wider probabilistic-programming ecosystem, where automatic-differentiation-friendly scoring lets a composed distribution drop into a Bayesian fit.

Where to learn more

• Want to get started running code? See the getting started guide.
• Want the right verb by intent? See the Concepts page.
• Want to understand the API? See the API reference.
• Want to chat about ComposedDistributions? Post on our GitHub Discussions.
• Want to see the code? Check out our GitHub repository.

Contributing

We welcome contributions and new contributors! This package follows ColPrac and the SciML style.

Supporting and citing

If you would like to support ComposedDistributions, please star the repository — such metrics help secure future funding.

If you use ComposedDistributions in your work, please cite it:

@software{ComposedDistributions_jl,
  author       = {Sam Abbott and EpiAware contributors},
  title        = {ComposedDistributions.jl},
  year         = {2026},
  doi          = {10.5281/zenodo.XXXXXXX}, # replace once released
  url          = {https://github.com/EpiAware/ComposedDistributions.jl}
}

Code of conduct

Please note that the ComposedDistributions project is released with a Contributor Code of Conduct. By contributing, you agree to abide by its terms.