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Comparison with Distributions.jl

A common first question is: how does ExponentialFamily.jl relate to Distributions.jl? The short answer is that ExponentialFamily.jl extends Distributions.jl — it does not replace it. Distributions.jl is a direct dependency, and the two are designed to be used together.

What each package is for

Distributions.jl is the foundational Julia package for probability distributions. It provides a broad "zoo" of distributions together with a unified interface for the operations you most often need:

  • sampling random values (rand),
  • evaluating densities and probabilities (pdf, logpdf, cdf),
  • summarising distributions (mean, var, params), and
  • fitting distributions to data (fit).

ExponentialFamily.jl focuses on the subset of distributions that belong to the exponential family and adds the specialised machinery that this shared structure makes possible:

  • a natural-parameter representation via the generic ExponentialFamilyDistribution type,
  • analytic products of distributions over the same variable (the core operation behind Bayes' rule and conjugate inference),
  • direct access to exponential family attributes — base measure, sufficient statistics, log partition function, and Fisher information, and
  • a number of extra parameterizations and distributions that are convenient for inference but are not part of Distributions.jl (see the Library page).

At a glance

Distributions.jlExponentialFamily.jl
ScopeDistributions of all kindsThe exponential family subset
ParameterizationMean parameters (e.g. mean, variance, probability)Natural parameters $\eta$, plus conversions to/from mean parameters
Sampling (rand)✔ Primary featureUses Distributions.jl
Density (pdf, logpdf)✔✔ (also in natural form)
Fitting to data (fit)✔Uses Distributions.jl
Analytic product of distributions—✔
Sufficient statistics / log partition / Fisher information—✔
RelationshipStandalone foundationBuilds on top of Distributions.jl

Using both together

Because ExponentialFamily.jl re-uses the Distributions.jl types directly, you move between the two worlds with a single convert call. Start from an ordinary Distributions.jl distribution defined by its familiar mean parameters:

using ExponentialFamily, Distributions

bernoulli = Bernoulli(0.25) # the usual Distributions.jl distribution
Bernoulli{Float64}(p=0.25)

Convert it into its exponential family (natural parameter) representation when you need the extra machinery:

ef = convert(ExponentialFamilyDistribution, bernoulli)
ExponentialFamily(Bernoulli)

And convert straight back to the Distributions.jl type when you are done:

convert(Bernoulli, ef)
Bernoulli{Float64}(p=0.25)

The round trip recovers the original distribution. In practice you will keep using Distributions.jl for sampling and density evaluation, and reach for ExponentialFamily.jl when you need products, sufficient statistics, or other exponential family attributes.

When should I use which?

  • Reach for Distributions.jl when you want to draw samples, evaluate a density, fit a distribution to data, or work with a distribution that is not in the exponential family.
  • Reach for ExponentialFamily.jl when you need to multiply distributions analytically (e.g. inside a Bayesian inference routine), or when you need the natural parameters, sufficient statistics, log partition function, or Fisher information of an exponential family member.

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