viva_math - v1.2.100

viva_math/distributions

Probability distributions.

Closed-form PDF / CDF / log-PDF + samplers backed by viva_math/random. All samplers are pure: they take a Seed and return a new seed.

Scope

Continuous: gaussian, uniform, exponential, cauchy, laplace. Discrete: bernoulli, categorical.

For heavier statistics (gamma, beta, chi-square) prefer gleam_stats or gleam_community_maths. Here we ship only what viva_emotion and viva_tensor consume directly.

Types

Bernoulli

</> 
pub type Bernoulli {
  Bernoulli(p: Float)
}

Constructors 

  • Bernoulli(p: Float)

Categorical

</> 
pub type Categorical {
  Categorical(probs: List(Float))
}

Constructors 

  • Categorical(probs: List(Float))

Cauchy

</> 
pub type Cauchy {
  Cauchy(location: Float, scale: Float)
}

Constructors 

  • Cauchy(location: Float, scale: Float)

Exponential

</> 
pub type Exponential {
  Exponential(rate: Float)
}

Constructors 

  • Exponential(rate: Float)

Gaussian

</>

Gaussian parameters.

pub type Gaussian {
  Gaussian(mean: Float, stddev: Float)
}

Constructors 

  • Gaussian(mean: Float, stddev: Float)

Laplace

</> 
pub type Laplace {
  Laplace(location: Float, scale: Float)
}

Constructors 

  • Laplace(location: Float, scale: Float)

Uniform

</> 
pub type Uniform {
  Uniform(low: Float, high: Float)
}

Constructors 

  • Uniform(low: Float, high: Float)

Values

bernoulli_pmf

</> 
pub fn bernoulli_pmf(b: Bernoulli, k: Int) -> Float

bernoulli_sample

</> 
pub fn bernoulli_sample(
  b: Bernoulli,
  seed: random.Seed,
) -> #(Bool, random.Seed)

categorical_entropy

</> 
pub fn categorical_entropy(c: Categorical) -> Float

Entropy H(X) = -Σ pᵢ log pᵢ.

categorical_pmf

</> 
pub fn categorical_pmf(c: Categorical, k: Int) -> Float

PMF for a category index (zero-based).

categorical_sample

</> 
pub fn categorical_sample(
  c: Categorical,
  seed: random.Seed,
) -> Result(#(Int, random.Seed), Nil)

cauchy_pdf

</> 
pub fn cauchy_pdf(c: Cauchy, x: Float) -> Float

cauchy_sample

</> 
pub fn cauchy_sample(
  c: Cauchy,
  seed: random.Seed,
) -> #(Float, random.Seed)

exponential_cdf

</> 
pub fn exponential_cdf(e: Exponential, x: Float) -> Float

CDF.

exponential_pdf

</> 
pub fn exponential_pdf(e: Exponential, x: Float) -> Float

PDF f(x; λ) = λ · e^(-λx) for x ≥ 0.

exponential_sample

</> 
pub fn exponential_sample(
  e: Exponential,
  seed: random.Seed,
) -> #(Float, random.Seed)

Inverse-CDF sampling.

Uses x = -log1p(-U) / λ, which is numerically equivalent to -ln(1 - U) / λ but avoids cancellation when U is near zero. Since random.uniform returns U ∈ [0, 1), 1 - U ∈ (0, 1] never hits zero.

gaussian_cdf

</> 
pub fn gaussian_cdf(g: Gaussian, x: Float) -> Float

Cumulative distribution F(x; μ, σ) = ½ · (1 + erf((x - μ)/(σ√2))).

gaussian_log_pdf

</> 
pub fn gaussian_log_pdf(g: Gaussian, x: Float) -> Float

Log-density. More numerically stable than ln(gaussian_pdf).

gaussian_pdf

</> 
pub fn gaussian_pdf(g: Gaussian, x: Float) -> Float

Probability density f(x; μ, σ) = 1/(σ√(2π)) · exp(-(x-μ)²/(2σ²)).

gaussian_sample

</> 
pub fn gaussian_sample(
  g: Gaussian,
  seed: random.Seed,
) -> #(Float, random.Seed)

Sample from a Gaussian.

laplace_pdf

</> 
pub fn laplace_pdf(l: Laplace, x: Float) -> Float

laplace_sample

</> 
pub fn laplace_sample(
  l: Laplace,
  seed: random.Seed,
) -> #(Float, random.Seed)

standard_normal

</> 
pub fn standard_normal() -> Gaussian

Standard normal N(0, 1).

uniform_cdf

</> 
pub fn uniform_cdf(u: Uniform, x: Float) -> Float

CDF.

uniform_pdf

</> 
pub fn uniform_pdf(u: Uniform, x: Float) -> Float

PDF on [low, high]; zero elsewhere.

uniform_sample

</> 
pub fn uniform_sample(
  u: Uniform,
  seed: random.Seed,
) -> #(Float, random.Seed)
✨ Search Document