feat(distributions): add LogNormal distribution#331
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Adds distrax.LogNormal(loc, scale) — the Log-Normal distribution on
(0, ∞), where log(X) ~ Normal(loc, scale).
The Log-Normal arises naturally wherever multiplicative noise is
present: financial returns, rainfall intensity, protein expression
levels, and many Bayesian model priors.
Implements:
- log_prob(x) = Normal(mu, sigma).log_prob(log x) − log x
- mean() = exp(μ + σ²/2)
- variance() = (exp(σ²)−1) * exp(2μ+σ²)
- mode() = exp(μ − σ²)
- median() = exp(μ)
- entropy() = μ + ½ + log(σ) + ½ log(2π) (exact closed form)
- kl_divergence(other): delegates to the underlying Normal KL when
other is also LogNormal (analytic, equals Normal KL in log-space)
Adds distrax.LogNormal to the public __init__.py and 17 tests covering
log_prob against both TFP and scipy, mean/variance/mode/median/entropy
against TFP, KL divergence, sample shape/positivity/moments, and JIT.
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What does this PR do?
Adds
distrax.LogNormal(loc, scale)— the Log-Normal distribution on (0, ∞). If X ~ LogNormal(μ, σ), then log(X) ~ Normal(μ, σ).The Log-Normal arises naturally in probabilistic ML wherever multiplicative noise is present: financial returns, rainfall, protein expression, and many Bayesian model priors. Unlike Beta/Gamma (bounded or semi-bounded), LogNormal covers the full positive real line with a simple reparameterizable sampler.
Implemented
log_prob(x)Normal(μ,σ).log_prob(log x) − log xmean()exp(μ + σ²/2)variance()(exp(σ²)−1) · exp(2μ+σ²)mode()exp(μ − σ²)median()exp(μ)entropy()μ + ½ + log(σ) + ½ log(2π)(exact)kl_divergencesample()exp(Normal(μ,σ).sample())— reparameterizableTests
17 tests in
log_normal_test.py: log_prob vs TFP and scipy, mean / variance / mode / median / entropy vs TFP, KL divergence (self=0, analytic vs TFP), sample shape, positivity, moments, JIT compatibility.