bf.dist.levy: Levy distribution

In BayesForge: Bayesian Inference using 'numpyro' and 'XLA'

Levy distribution

Description

The Levy distribution (or L\'evy) is a continuous probability distribution on the positive real line (or shifted positive line) that is heavy-tailed, skewed, and arises naturally in connection with stable distributions, specifically the case with stability index \alpha = 1/2. It is often used in contexts such as hitting-time problems for Brownian motion, physics (e.g., van der Waals line-shapes), and modelling very heavy-tailed phenomena. Let X be a Levy-distributed random variable with location parameter \mu and scale parameter c > 0. The support is x \ge \mu.

Usage

bf.dist.levy(
  loc,
  scale,
  validate_args = py_none(),
  name = "x",
  obs = py_none(),
  mask = py_none(),
  sample = FALSE,
  seed = py_none(),
  shape = c(),
  event = 0,
  create_obj = FALSE,
  to_jax = TRUE
)

Arguments

loc	A numeric vector, matrix, or array representing the location parameter.
scale	A numeric vector, matrix, or array representing the scale parameter.
validate_args	Logical: Whether to validate parameter values. Defaults to 'reticulate::py_none()'.
name	A character string representing the name of the random variable within a model. This is used to uniquely identify the variable. Defaults to 'x'.
obs	A numeric vector or array of observed values. If provided, the random variable is conditioned on these values. If 'NULL', the variable is treated as a latent (unobserved) variable. Defaults to 'NULL'.
mask	A logical vector, matrix, or array to mask observations.
sample	A logical value that controls the function's behavior. If 'TRUE', the function will directly draw samples from the distribution. If 'FALSE', it will create a random variable within a model. Defaults to 'FALSE'.
seed	An integer used to set the random seed for reproducibility when 'sample = TRUE'. This argument has no effect when 'sample = FALSE', as randomness is handled by the model's inference engine. Defaults to 0.
shape	A numeric vector used for shaping. When ‘sample=FALSE' (model building), this is used with '.expand(shape)' to set the distribution’s batch shape. When 'sample=TRUE' (direct sampling), this is used as 'sample_shape' to draw a raw JAX array of the given shape.
event	Integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
create_obj	Logical; If 'TRUE', returns the raw BI distribution object instead of creating a sample site.
to_jax	Logical. Defaults to TRUE.

Value

• When sample=FALSE, a BI Levy distribution object (for model building).

• When sample=TRUE, a JAX array of samples drawn from the Levy distribution (for direct sampling).

• When create_obj=TRUE, the raw BI distribution object (for advanced use cases).

See Also

This is a wrapper of https://num.pyro.ai/en/stable/distributions.html#levy

Examples

library(BayesForge)
m <- importBF(platform = "cpu")
bf.dist.levy(loc = 1, scale = 10, sample = TRUE)

BayesForge documentation built on June 9, 2026, 1:09 a.m.