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