bf.dist.lower_truncated_power_law: Lower Truncated Power Law Distribution

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

Lower Truncated Power Law Distribution

Description

The *Lower-Truncated Power-Law* distribution (also known as the *Pareto Type I* or *power-law with a lower bound*) models quantities that follow a heavy-tailed power-law behavior but are bounded below by a minimum value

x_{\min}

. It is commonly used to describe phenomena such as wealth distributions, city sizes, and biological scaling laws.

Usage

bf.dist.lower_truncated_power_law(
  alpha,
  low,
  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

alpha	A numeric vector: index of the power law distribution. Must be less than -1.
low	A numeric vector: lower bound of the distribution. Must be greater than 0.
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: Optional boolean 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: A multi-purpose argument 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: 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. This is essential for building complex distributions like 'MixtureSameFamily'.
to_jax	Boolean. Indicates whether to return a JAX array or not.

Value

- When sample=FALSE, a BI Lower Truncated Power Law distribution object (for model building).

- When sample=TRUE, a JAX array of samples drawn from the Lower Truncated Power Law 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#lowertruncatedpowerlaw

Examples

library(BayesForge)
m <- importBF(platform = "cpu")
bf.dist.lower_truncated_power_law(alpha = c(-2, 2), low = c(1, 0.5), sample = TRUE)

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