bf.dist.pareto: Samples from a Pareto distribution.

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

Samples from a Pareto distribution.

Description

The **Pareto distribution**, named after economist Vilfredo Pareto, is a **power-law** probability distribution used to describe phenomena with "rich-get-richer" or "heavy-tail" properties - for example, income distribution, city sizes, or wealth concentration. It is characterized by: * a **scale parameter**

x_m > 0

(the minimum possible value), and * a **shape parameter**

\alpha > 0

(which controls the tail heaviness). A random variable

X \sim \text{Pareto}(\alpha, x_m)

takes values

x \ge x_m

.

Usage

bf.dist.pareto(
  scale,
  alpha,
  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

scale	A numeric vector or single number representing the scale parameter of the Pareto distribution. Must be positive.
alpha	A numeric vector or single number representing the shape parameter of the Pareto distribution. Must be positive.
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. 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	An integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
create_obj	A logical value. 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 Pareto distribution object (for model building).

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

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

See Also

https://num.pyro.ai/en/stable/distributions.html#pareto

Examples

library(BayesForge)
m=importBF(platform='cpu')
bf.dist.pareto(scale = c(0.2, 0.5, 0.8), alpha = c(-1.0, 0.5, 1.0), sample = TRUE)

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