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• R package: algebraic.dist
  • Installation
  • Overview
    • Distribution types
    • Automatic simplification
    • Multivariate operations
    • Limiting distributions
  • Quick example
  • Documentation

R package: algebraic.dist

An algebra over probability distributions: compose, transform, and automatically simplify distribution expressions in R.

Tags: probability distributions, distribution algebra, automatic simplification, multivariate normal, mixture models, CLT, delta method, Monte Carlo, R, statistics

Installation

Install the stable release from CRAN:

install.packages("algebraic.dist")

Or install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("queelius/algebraic.dist")

Overview

algebraic.dist lets you build and manipulate probability distributions as first-class R objects. Algebraic operations (+, -, *, /, ^, exp, log, min, max, …) on distribution objects automatically simplify to closed-form distributions when mathematical identities apply, and fall back to lazy Monte Carlo expressions (edist) otherwise.

Distribution types

Normal, exponential, gamma, Weibull, chi-squared, uniform, beta, log-normal, Poisson, multivariate normal (MVN), mixture, and empirical distributions.

Automatic simplification

Over 20 built-in rules, including:

• Normal + Normal → Normal
• Gamma + Gamma (same rate) → Gamma
• exp(Normal) → LogNormal
• Normal(0,1)^2 → ChiSq(1)
• min(Exp, ..., Exp) → Exp
• c * Uniform(a,b) → Uniform

When no rule matches, the result is a lazy edist that samples from its components and evaluates the expression on demand.

Multivariate operations

• MVN conditioning: closed-form Schur complement via conditional()
• Affine transforms: affine_transform(x, A, b) for exact linear maps
• Mixture conditioning: Bayesian weight updates via Bayes’ rule
• Marginals: exact for MVN and mixture distributions

Limiting distributions

• clt() — Central Limit Theorem
• lln() — Law of Large Numbers
• delta_clt() — delta method for transformed means
• normal_approx() — moment-matching normal approximation

Quick example

library(algebraic.dist)

# Sum of normals simplifies to a normal
x <- normal(1, 4)
y <- normal(2, 5)
z <- x + y
z
#> Normal distribution (mu = 3, var = 9)

# exp of a normal simplifies to log-normal
w <- exp(normal(0, 1))
w
#> Log-normal distribution (meanlog = 0, sdlog = 1)

# Gamma addition with matching rates
g <- gamma_dist(3, 2) + gamma_dist(4, 2)
g
#> Gamma distribution (shape = 7, rate = 2)

# CLT: the standardized sample mean converges to N(0, 1)
clt(normal(5, 4))
#> Normal distribution (mu = 0, var = 4)

Documentation

The full documentation is available at https://queelius.github.io/algebraic.dist/.

Vignettes:

• Getting started — core distribution objects, sampling, and basic operations
• Distribution algebra — simplification rules, limiting distributions, and the CLT/LLN/delta method
• Multivariate operations — MVN conditioning, affine transforms, and Gaussian mixture models

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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