Univariate Distributions

All 16 univariate distributions share the Distribution base-class API (src/distributions/base.py):

pdf(x) · cdf(x) · ppf(q) · rvs(size, random_state) · mean() · var() · std() · median() · mode() · skewness() · kurtosis() · entropy() · interval(alpha) · get_statistics() · support() · parameter getters/setters with validated bounds (get_parameter_bounds()).

Continuous (10)

Distribution	Parameters	Support	Typical use
Normal	μ, σ	(−∞, ∞)	measurement error, CLT
Exponential	λ (rate)	[0, ∞)	inter-arrival times
Uniform	a, b	[a, b]	bounded ignorance prior
Beta	α, β	[0, 1]	proportions, Bayesian rates
Gamma	shape k, scale θ	[0, ∞)	waiting times, claims
Chi-Square	df	[0, ∞)	variance inference
Student-t	df	(−∞, ∞)	heavy tails, small samples
Weibull	shape, scale	[0, ∞)	reliability, lifetimes
Lognormal	μ, σ	(0, ∞)	incomes, sizes
Cauchy	x₀, γ	(−∞, ∞)	heavy-tail counterexample (mean/variance undefined → nan)

Discrete (6)

Distribution	Parameters	Support	Typical use
Binomial	n, p	{0..n}	successes in n trials
Poisson	λ	{0, 1, …}	counts, arrivals
Geometric	p	{1, 2, …}	trials until first success
Negative Binomial	n, p	{n, n+1, …}	trials until n-th success
Hypergeometric	M, n, N	bounded	sampling without replacement
Discrete Uniform	a, b	{a..b}	fair dice

Recipes

from probviz.distributions import NormalDistribution, PoissonDistribution

n = NormalDistribution(mu=0, sigma=1)
print(n.interval(0.95))      # 95% central interval
print(n.ppf(0.975))          # quantile
print(n.get_statistics())    # everything at once

pois = PoissonDistribution(lambda_param=3.0)
print(pois.pmf if hasattr(pois, "pmf") else pois.pdf([0, 1, 2, 3]))

Cauchy moments

Skewness/kurtosis/mean/variance are undefined for Cauchy; the API surfaces nan from SciPy rather than masking it. get_statistics() includes the nan so downstream code can decide how to handle it.

Mode search

mode() falls back to a bounded grid search when SciPy has no closed form. For heavy-tailed or infinite-support discretes the grid is intentionally bounded; treat mode() as an approximation there.