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Probability distributions
The distributions fall into three categories:
- Discrete distributions assign probability to countable values.
- Continuous distributions assign probability to uncountable values on a continuum.
- Prior distributions assign probability to other probability distributions.
Structs§
- Bernoulli distribution with success probability p
- Beta distribution, Beta(α, β) over x in (0, 1).
- Beta Binomial distribution over k in {0, …, n}
- Binomial distribution with success probability p
- Categorical distribution over unordered values in [0, k).
- Cauchy distribution over x in (-∞, ∞).
- Χ2 distribution Χ2(k).
- Chinese Restaurant Process, a distribution over partitions.
- Dirichlet distribution over points on the k-simplex.
- Discrete uniform distribution, U(a, b) on the interval x in [a, b]
- An empirical distribution derived from samples.
- Exponential distribution, Exp(λ) over x in [0, ∞).
- Gamma distribution G(α, β) over x in (0, ∞).
- Gaussian / Normal distribution, N(μ, σ) over real values.
- Geometric distribution over x in {0, 1, 2, 3, … }.
- Generalized Extreme Value Distribution Gev(μ, σ, ξ) where the parameters are μ is location σ is the scale ξ is the shape
- Χ-2 distribution Χ-2(v).
- Inverse gamma distribution IG(α, β) over x in (0, ∞).
- Inverse Gaussian distribution, N-1(μ, λ) over real values.
- Inverse Wishart distribution, W-1(Ψ,ν) over positive definite matrices.
- Kolmogorov-Smirnov distribution where the number of samples, $N$, is assumed to be large.
- Kumaraswamy distribution, Kumaraswamy(α, β) over x in (0, 1).
- Laplace, or double exponential, distribution over x in (-∞, ∞).
- LogNormal Distribution If x ~ Normal(μ, σ), then e^x ~ LogNormal(μ, σ).
- Mixture distribution Σ wi f(x|θi)
- Negative Binomial distribution NBin(r, p).
- Prior for Gaussian
- Prior for Gaussian
- Prior for Gaussian
- Common conjugate prior on the μ and Σ parameters in the Multivariate Gaussian, Ν(μ, Σ)
- Pareto distribution Pareto(x_m, α) over x in (x_m, ∞).
- Poisson distribution over x in {0, 1, … }.
- Scaled Χ-2 distribution Scaled-Χ-2(v, τ2).
- Skellam distribution over x in {.., -2, -1, 0, 1, … }.
- Student’s T distribution over x in (-∞, ∞).
- Symmetric Dirichlet distribution where all alphas are the same.
- Continuous uniform distribution, U(a, b) on the interval x in [a, b]
- UnitPowerLaw(α) over x in (0, 1).
- VonMises distribution on the circular interval (0, 2π]
Enums§
- Negative Binomial distribution errors