ModifiedDistributions.jl

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ModifiedDistributions ​

Wrappers for Distributions.jl univariate distributions that each change one behaviour — rescaling, likelihood weighting, hazard modification, or a forward transform — while everything else keeps working, plus the generic get_dist unwrap protocol.

Why ModifiedDistributions? ​

  • Rescale and shift — exact affine transforms of any univariate distribution, with the full distribution interface intact.

  • Weight likelihoods — scale an observation's contribution with weight while the result stays a real, samplable distribution, so a Turing.jl model (or any PPL built on Distributions.jl) remains a complete generative model.

  • Modify hazards — proportional or additive hazard changes with modify, in closed form.

  • Forward transforms — carry thinning or accumulation for a downstream count series without touching the distribution itself.

  • Unwrap anywhere — recover the distribution underneath any wrapper with get_dist.

  • Works with composed chains — modifiers apply across ComposedDistributions.jl chains.

  • AD-ready — tested in CI against ForwardDiff, ReverseDiff, Enzyme, and Mooncake.

Getting started ​

See documentation for a full walkthrough.

An affine transform gives the exact distribution of Y = 2X + 1, and the whole distribution interface follows:

julia
using ModifiedDistributions, Distributions

d = affine(LogNormal(1.5, 0.5); scale = 2.0, shift = 1.0)
(mean = mean(d), logpdf = logpdf(d, 5.0), median = quantile(d, 0.5))
(mean = 11.156838074360163, logpdf = -2.914108658241349, median = 9.963378140676129)

Weighting scales the log-likelihood contribution of an observation seen 10 times. The two numbers printed below match, showing the weighted log-density is exactly 10 times the base:

julia
wd = weight(d, 10.0)
(weighted = logpdf(wd, 5.0), manual = 10.0 * logpdf(d, 5.0))
(weighted = -29.141086582413493, manual = -29.141086582413493)

Hazard modification works in closed form. Halving the hazard raises the survival function to the power one half, and the two printed values agree:

julia
md = modify(LogNormal(1.5, 0.5), -log(2.0))
(modified = ccdf(md, 2.0), base_sqrt = ccdf(LogNormal(1.5, 0.5), 2.0)^0.5)
(modified = 0.9729873354092063, base_sqrt = 0.9729873354092063)

Unwrapping the weighted distribution returns the affine transform underneath:

julia
get_dist(wd)
Affine(Distributions.LogNormal{Float64}(μ=1.5, σ=0.5))

Relationship to Distributions.jl ​

Distributions.jl already supports affine arithmetic on some distributions (2.0 * X + 1.0) by returning a new parameterisation where one exists. affine instead wraps any univariate distribution with the exact change-of-variables maths, so it works uniformly and keeps the inner distribution recoverable via get_dist. Likewise weight replaces ad hoc n * logpdf(d, x) terms in model code with a distribution object that carries its weight, and modify gives hazard-scale transforms that have no Distributions.jl counterpart.

What packages work well with ModifiedDistributions.jl? ​

  • Distributions.jl supplies the distributions being modified.

  • Turing.jl and other PPLs consume the wrappers directly, e.g. weighted likelihoods for aggregated data.

  • ComposedDistributions.jl composes distributions into chains; a package extension lets the modifier verbs apply across a chain's observed total.

  • CensoredDistributions.jl and the wider EpiAware ecosystem build censoring, convolution, and composition layers on top of these modifiers.

Where to learn more ​

Contributing ​

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

Supporting and citing ​

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

If you use ModifiedDistributions in your work, please cite it (the DOI is a placeholder until the first Zenodo release):

bibtex
@software{ModifiedDistributions_jl,
  author       = {Sam Abbott and EpiAware contributors},
  title        = {ModifiedDistributions.jl},
  year         = {2026},
  doi          = {10.5281/zenodo.XXXXXXX},
  url          = {https://github.com/EpiAware/ModifiedDistributions.jl}
}

Code of conduct ​

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