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algebraic.dist 0.9.1

New Generics

• as_dist() — S3 generic for converting objects (e.g., fitted models) into dist objects. Identity method for dist; designed as an extension point for downstream packages

Unified Fallback Layer

• realized_dist subclass of empirical_dist — preserves provenance (source distribution, sample count) when materializing via Monte Carlo
• ensure_realized() internal memoized entry point — all MC fallback methods now share cached samples (calling cdf(e) + density(e) on the same edist no longer draws independent samples)
• conditional.dist and rmap.dist now route through ensure_realized() for consistent provenance

New Simplification Rules

• Uniform(a,b) + c → Uniform(a+c, b+c) (location shift)
• Uniform(a,b) - c → Uniform(a-c, b-c) (location shift)
• c * Uniform(a,b) → Uniform(min(ca,cb), max(ca,cb)) for c ≠ 0
• c * Weibull(k,λ) → Weibull(k, c*λ) for c > 0
• c * ChiSq(df) → Gamma(df/2, 1/(2c)) for c > 0
• c * LogNormal(μ,σ) → LogNormal(μ+log(c), σ) for c > 0
• LogNormal * LogNormal → LogNormal(μ₁+μ₂, √(σ₁²+σ₂²))
• -Uniform(a,b) → Uniform(-b, -a) (unary negation)

New Operators

• /.dist — Division operator: dist / scalar delegates to scalar multiplication rules; scalar / dist and dist / dist create edist

MVN Algebra

• conditional.mvn — closed-form Schur complement conditioning with given_indices/given_values, or predicate-based MC fallback
• affine_transform(x, A, b) — compute AX + b for normal/MVN distributions (exact)

Mixture Multivariate

• marginal.mixture — marginal of mixture is mixture of marginals (exact)
• conditional.mixture — Bayes’ rule weight update for mixture-of-MVN conditioning, with predicate-based MC fallback

Limiting Distributions

• clt(base_dist) — CLT limiting distribution: Normal(0, Var) or MVN(0, Σ)
• lln(base_dist) — LLN degenerate limit: Normal(μ, 0) or MVN(μ, 0)
• delta_clt(base_dist, g, dg) — delta method with user-supplied derivative/Jacobian
• normal_approx(x) — moment-matching normal approximation of any distribution

algebraic.dist 0.2.0

New Distributions

• gamma_dist(shape, rate) — Gamma distribution with hazard/survival functions
• weibull_dist(shape, scale) — Weibull distribution with closed-form hazard
• chi_squared(df) — Chi-squared distribution with hazard/survival functions
• uniform_dist(min, max) — Uniform distribution on [min, max]
• beta_dist(shape1, shape2) — Beta distribution on (0, 1)
• lognormal(meanlog, sdlog) — Log-normal distribution with hazard/survival
• poisson_dist(lambda) — Poisson distribution with exact expectation via truncated summation
• mixture(components, weights) — Mixture distributions with law of total variance

New Operators and Algebra

• *.dist — Scalar multiplication (c * dist, dist * c, dist * dist)
• ^.dist — Power operator (dist ^ n)
• Math.dist — Group generic for exp(), log(), sqrt(), abs(), etc.
• Summary.dist — Group generic for sum(), prod(), min(), max()
• Extended +.dist and -.dist for numeric location shifts

Simplification Rules

• c * Normal(mu, v) simplifies to Normal(c*mu, c^2*v)
• c * Gamma(a, r) simplifies to Gamma(a, r/c) for c > 0
• c * Exponential(r) simplifies to Gamma(1, r/c) for c > 0
• Normal(mu, v) + c simplifies to Normal(mu+c, v)
• Gamma(a1, r) + Gamma(a2, r) simplifies to Gamma(a1+a2, r) (same rate)
• Exp(r) + Exp(r) simplifies to Gamma(2, r) (same rate)
• ChiSq(d1) + ChiSq(d2) simplifies to ChiSq(d1+d2)
• Poisson(l1) + Poisson(l2) simplifies to Poisson(l1+l2)
• Normal(0,1)^2 simplifies to ChiSq(1)
• exp(Normal(mu, v)) simplifies to LogNormal(mu, sqrt(v))
• log(LogNormal(ml, sl)) simplifies to Normal(ml, sl^2)
• min(Exp(r1), ..., Exp(rk)) simplifies to Exp(sum(r))

New Infrastructure

• realize() generic — materialize any distribution to empirical_dist by sampling
• Auto-fallback methods for edist: cdf, density, sup, conditional, rmap, inv_cdf
• countable_set R6 class for countably infinite support (Poisson)
• inv_cdf.empirical_dist — quantile function for empirical distributions

Improvements

• Informative error messages in all constructors (replaced stopifnot)
• format() methods for all distribution types
• Standardized print() methods delegating to format()
• Fixed vcov.exponential — was returning rate instead of 1/rate^2
• Fixed sampler.edist crash when n=1
• conditional.empirical_dist gives informative error on zero matches
• Zero-variance guard in expectation_data() CI computation

algebraic.dist 0.1.0

• Initial CRAN release.

Features

• Core distribution types: normal, mvn, exponential, empirical_dist
• Expression distributions (edist) for lazy composition of distributions
• Algebraic operations (+, -) on distributions with automatic simplification
• Support classes: finite_set, interval for representing distribution domains
• Generic methods: sampler, mean, vcov, density, cdf, params
• Monte Carlo estimation for expectation, conditional, and rmap operations

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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